Browse Quadratics problems Studdy Solved!

Problem 1001

Solve the equation $-9 x^{2}=-8 x+8$ .

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Problem 1002

Factor the expression $b^{2}-9$ completely over the integers.

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Problem 1003

Rewrite the expression $2x^{2}-8x+5$ as $a(x-h)^{2}+k$ .

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Problem 1004

How do the signs of $b$ and $c$ in $x^{2}+b x+c$ affect $p$ and $q$ in $(x+p)(x+q)$ ?

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Problem 1005

Shift the function $g(x)=4 x^{2}-16$ 9 units right and 1 down. What is the new equation? A. $h(x)=4(x+9)^{2}-17$ B. $h(x)=4(x-17)^{2}-9$ C. $h(x)=4(x-9)^{2}-17$ D. $h(x)=4(x-7)^{2}+16$

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Problem 1006

Solve $x^{2}=36$ . Which solutions are correct? Select all that apply: $x=6$ , $x=36^{2}$ , $x=-6$ , $x=18$ , $x=-18$ .

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Problem 1007

Solve $x^{2}=16$ and select all correct answers: $x=-4$ , $x=4$ , $x=-8$ , $x=16^{2}$ , $x=8$ .

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Problem 1008

Solve $x^{2}=81$ . Which solutions are correct? Select all that apply: $x=9$ , $x=-9$ , $x=7$ , $x=-7$ .

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Problem 1009

Find the solutions for $x^{2}=9$ . Select all correct answers: $x=18$ , $x=81$ , $x=-81$ , $x=-3$ , $x=3$ .

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Problem 1010

Solve $x^{2}=25$ . Which solutions are correct? Choose all that apply: $x= \pm \sqrt{5}$ , $x=25$ , $x=5$ , $x=-25$ , $x=-5$ .

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Problem 1011

Solve $x^{2}=144$ . Which solutions are correct? Choose all that apply: $x=72$ , $x=12$ , $x=-72$ , $x=11$ , $x=-12$ .

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Problem 1012

Find $h(6)$ if $h(x) = x^{2} - 4$ .

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Problem 1013

Find the $y$ -coordinate of the vertex of the parabola $g$ given points (-1, 1), (3, 9), (4, 6) and $x=2$ .

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Problem 1014

Find the value of $k$ for the quadratic function $y=f(x)$ passing through $(5,1),(7,k),(9,26)$ with average rate change of 1.5.

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Problem 1015

Find the quadratic equation $f(x)$ that matches the points: $(-1, 10)$ , $(0, 14)$ , and $(1, 20)$ .

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Problem 1016

What transformation changes $f(x)=2x^{2}+10$ to $g(x)=8x^{2}+10$ ?

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Problem 1017

Identify the transformation that changes $f(x)=3(x-6)^{2}$ into $g(x)=3x^{2}+10$ .

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Problem 1018

Identify the transformation that changes $f(x)=8 x^{2}-8$ to $g(x)=x^{2}-1$ .

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Problem 1019

Identify the transformation that changes $f(x)=10 x^{2}-5$ to $g(x)=2 x^{2}-1$ .

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Problem 1020

Match each expression to its factored form:
1. $-x^{2}-y^{2}$
2. $-x^{2}+2xy+y^{2}$
3. $-x^{2}-2xy+y^{2}$
4. $-x^{2}+y^{2}$
a. $(x-y)^{2}$ b. $(x+y)^{2}$ c. $(x+y)(x-y)$ d. prime

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Problem 1021

Expand $(2 x-3)^{2}$ . Choose from: $4 x^{2}-9$ , $4 x^{2}+9$ , $2 x^{2}-12 x+9$ , $4 x^{2}-12 x+9$ .

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Problem 1022

Find the average rate of change of the function $f(x)=x^{2}+6x+10$ over the interval $[-2,1]$ .

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Problem 1023

Solve by factoring: $x^{2}+5x+6=0$ . Find the roots. Options: $-3,-2$ ; $3,2$ ; $-3,2$ ; $3,-2$ .

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Problem 1024

Factor the quadratic $x^{2}+14x+45$ . Choose from the options: $(x+9)(x+5)$ , $(x+9)(x-5)$ , $(x+10)(x+4)$ , $(x+8)(x+6)$ .

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Problem 1025

Determine if the function $h(x)=x^{2}+1$ is even, odd, or neither using algebraic methods.

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Problem 1026

A ball's height after $t$ seconds is $h(t)=144t-16t^{2}$ . What does $h(2)=224$ mean?

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Problem 1027

Find the quadratic function $h(t)$ for a ball that reaches 16 feet at 1 second and returns to the ground at 2 seconds.

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Problem 1028

Factoriza $(x+y)^{2}-z^{2}$ .

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Problem 1029

Solve the equation $x^{2}+5x+1=0$ and round your answers to one decimal place.

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Problem 1030

Determine the direction in which the parabola $y=-\frac{1}{3} x^{2}+2$ opens.

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Problem 1031

Find the zeros of the equation $y=4x^{2}-36$ . List the values of $x$ separated by commas.

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Problem 1032

Find the end behavior of $y$ as $x \to \infty$ for $y = -2x^{2} + 4x + 2$ .

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Problem 1033

The parabola $y=3 x^{2}+4$ opens upwards.

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Problem 1034

Determine the direction in which the parabola $x=\frac{2}{3} y^{2}-3$ opens.

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Problem 1035

Find the value(s) of $x$ when $y=3$ in the equation $y=2x^2-5$ .

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Problem 1036

Find where the polynomial $y=x^{2}+3x+2$ intersects the $y$ -axis.

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Problem 1037

Find the $x$ -values where $y = x^{2} + 5x + 6$ intersects the $x$ -axis. (List answers separated by commas.)

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Problem 1038

Find the points where the polynomial $y=x^{2}-4 x+3$ intersects the $\mathrm{x}$ -axis.

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Problem 1039

Use the graph of the quadratic function $f$ to determine the solution. (a) Solve $f(x)>0$ . (b) Solve $f(x) \leq 0$ . (a) The solution to $f(x)>0$ is $\square$ (Type your answer in interval notation.)

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Problem 1040

4. Discriminant and solutions of a quadratic equation from a graph
Given the discriminant, match it to its graph, then give the reason for your selection

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Problem 1041

Given the function defined by $g(x)=-x^{2}+3 x+3$ , find $g(-2)$ . Simplify. $g(-2)=$ $\square$

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Problem 1042

Given the function defined by $g(x)=3 x^{2}-7 x+3$ , find $g(-2 x)$ . Express the answer in simplest form. $g(-2 x)=$

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Problem 1043

Solve the polynomial inequality and graph the solution set on a real number line. Express the solution set in interval notation. $x^{2}+8 x+15>0$

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Problem 1044

Use set-builder notation to describe the domain and range of the function.
Describe the domain of the function. If multiple correct answers are possible, use the narrowest possible answer. Select the correct choice below and, if necessary, fill in the answer box(es) within your choice. A. $\{x \mid x$ is an integer and $\leq x \leq\}$
79. $\{x \mid x<\}$ C. $\{x \mid x \geq$ $\square$ E. $\{x \mid x$ is an odd integer and $\leq x \leq\}$
G. $\{x \mid x \leq\}$
$\{x \mid x>\}$
Describe the range of the function. If multiple correct answers are possible, use the narrowest possible ${ }^{\text {I }}$ . choice. A. $\{y \mid y$ is an odd integer and $\square$ sys $\square$ $\{x \mid x$ is an even integer and $\square$ sxs \} C. $\{y \mid y \geq$ $\square$ E. $\{y \mid y$ is an integer and $\square$ sys $\square$ B. $\{y \mid y \leq$ $\square$ D. $\{y \mid y$ is an even integer and $\square \leq y \leq\}$ $\square$ $\square$ F. $\{y \mid y<\square\}$ G. $\{y|y\rangle$ $\square$ H. $\{y \mid y$ is a real number $\}$

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Problem 1045

Solving a word problem usting a quinalauct
A model rocket is launched with an initial upward velocity of $215 \mathrm{ft} / \mathrm{s}$ . The rockets height $h$ (in feet) after $t$ seconds is given by the following. Espan $h=215 t-16 t^{2}$
Find all values of $t$ for which the rocket's height is 97 feet. Round your answer(s) to the nearest hundredth. (if there is more than one answer, use the "or" button.) $t=\square \text { seconds }$ $\square$ or $\square$

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Problem 1046

If an object is projected upward with an initial velocity of 123 ft per sec, its height h after t seconds is $\mathrm{h}=-16 \mathrm{t}^{2}+123 \mathrm{t}$ . Find the height of the object after 2 seconds.
The height of the object after 2 seconds is $\square$ (Simplify your answer.)

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Problem 1047

Factor completely. $c^{2}-12 c+36$
Select the correct choice below and fill in any answer boxes within your choice. A. $c^{2}-12 c+36=$ $\square$ B. The expression is prime.

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Problem 1048

Factor completely. $r^{2}+25$
Select the correct choice below and fill in any answer boxes within your choice. A. The answer is $\square$ . B. The expression is prime.

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Problem 1049

Solve the quadratic equation by completing the square. $x^{2}+2 x=15$
The solution set is $\square$ \}. (Type an integer or a simplified fraction. Use a comma to separate answers as needed.)

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Problem 1050

The roots of the equation $a x^{2}+b x+c=0$ are $-\frac{1}{2}$ and $-\frac{3}{2}$ . Find the values of $a, b$ and $c$ .
The interior angles of a polygon are: $(2 t+1)^{\circ},(3 t-2)^{\circ},(4 t)^{\circ}(5 t-2)^{\circ},(2 t-1)^{\circ}$ and $(3 t+2)^{\circ}$ . Find the: (i) value of $t$ , (ii) difference between the largest and smallest angle.

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Problem 1051

Solve using the quadratic formula. $9 r^{2}+6 r+1=0$

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Problem 1052

Solve for $x$ and graph the solution. $-34 x^{2}-13 x+46 \leq-33 x^{2}-13 x+37$
Plot the endpoints. Select an endpoint to change it from closed to open. Select the middle of a segment, ray, or line to delete it. Submit

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Problem 1053

Lessons Assessments Gradebook Email 1 Tools My Courses (02.04, 2:07 HC)
An interior designer wants to decorate a newly constructed house. The function $f(x)=49 x^{2}-200$ represents the amount of money he earns per room decorated, where $x$ represents the number of rooms he designs. The function $g(x)=\frac{1}{7} x$ represents the number of rooms the interior designer decorates, where $x$ is the number of hours he works.
Part A: Determine the amount of money the interior designer will make decorating the house as a function of hours he works. (5 points) Part B: If the newly constructed house requires 50 hours of work, how much will the interior designer earn? Show all necessary calculations. (5 points) Part C: Determine an expression to represent the difference quotient for the function found in Part A. Show all necessary work. (5 points)

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Problem 1054

Solve for $x$ and graph the solution. $x^{2}-7>4 x-2$
Plot the endpoints. Select an endpoint to change it from closed to open. Select the middle of a segment, ray, or line to delete it. Submit

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Problem 1055

Question 30 of 60
Use the quadratic formula to solve the equation. $5 x^{2}-2 x=1$
The solution set is $\square$ B. (Simplify your answer. Type an exact answer, using radicals and $i^{\prime}$ as needed. Use integers or fractions for ar

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Problem 1056

8. For the function $f(x)=2(x-3)^{2}+2$ , determine the location of the vertex and the $\mathbf{x}$ and y -intercepts.

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Problem 1057

a.) Calculate the discriminant by hand and state the rumber and type of solutions to the equation $x^{2}+2 x=2$

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Problem 1058

Solve $x^{2}+2 x=2$ , using the quadratic formula (show as much work as possible). Remember the quadratic formula is: $x=\frac{-b \pm \sqrt{b^{2}-4 a c}}{2 a}$ .

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Problem 1059

Find the minimum value of the parabola $y=x^{2}+4 x+1$
Simplify your answer and write it as a proper fraction, improper fraction, or integer. $\square$

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Problem 1060

Factor the equation $y = x^2 + 5x + 1$ .

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Problem 1061

Übung 1 Untersuchung einer Kurvenschar Gegeben ist die Kurvenschar $\mathrm{f}_{\mathrm{a}}(\mathrm{x})=\mathrm{x}^{2}-(\mathrm{a}+1) \cdot \mathrm{x}+\mathrm{a}(\mathrm{a} \in \mathbb{R}, \mathrm{a} \geq 1)$ . a) Untersuchen Sie $f_{a}$ auf Nullstellen und Extremstellen. b) Skizzieren Sie die Graphen von $f_{1}, f_{2}$ und $f_{3}$ für $-1 \leq x \leq 4$ . c) Welche Kurve der Schar $f_{a}$ hat an der Stelle $x=2$ ein lokales Extremum? d) Welche Kurve der Schar $f_{a}$ hat genau eine Nullstelle?

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Problem 1062

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7. Simplifying tho quadratic formula complete the next otrepe tio fimal the collutinst Fin) simplym the malicul if nerind Th) Simplify the equation if encthet

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Problem 1063

Simplify. (a) $(4-\sqrt{5})^{2}$ $\square$ (b) $(10+2 \sqrt{7})^{2}$ $\square$

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Problem 1064

The graph shows $g(x)$ , which is a translation of $f(x)=x^{2}$ . Write the function rule for $g(x)$ .
Write your answer in the form $\mathrm{a}(\mathrm{x}-\mathrm{h})^{2}+\mathrm{k}$ , where $\mathrm{a}, \mathrm{h}$ , and k are integers or simplified fractions.

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Problem 1065

Part 1 of 11
For the quadratic function $f(x)=x^{2}+6 x$ , answer parts (a) through ( $f$ ). (a) Find the vertex and the axis of symmetry of the quadratic function, and determine whether the graph is concave up or concave down.
The vertex is $\square$ (Type an ordered pair, using integers or fractions.)

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Problem 1066

Part 4 of 11
For the quadratic function $f(x)=x^{2}+6 x$ , answer parts (a) through (f). (a) Find the vertex and the axis of symmetry of the quadratic function, and determine whether the graph is concave up or concave down.
The vertex is $(-3,-9)$ . (Type an ordered pair, using integers or fractions.) What is the equation of the axis of symmetry? The axis of symmetry is $x=-3$ . (Use integers or fractions for any numbers in the equation.) Is the graph concave up or concave down? Concave down Concave up (b) Find the $y$ -intercept and the $x$ -intercepts, if any.
What is the $y$ -intercept? Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. The $y$ -intercept is $\square$ (Type an integer or a simplified fraction.) B. There is no $y$ -intercept.

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Problem 1067

$f(x)=-3 x^{2}+6 x$
The quadratic function has a $\square$ value.

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Problem 1068

$f(x)=3 x^{2}+24 x-3$
Does the quadratic function $f$ have a minimum value or a maximum value? The function $f$ has a maximum value. The function $f$ has a minimum value.

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Problem 1069

$f(x)=3 x^{2}+24 x-3$
Does the quadratic function $f$ have a minimum value or a maximum value? The function $f$ has a maximum value. The function $f$ has a minimum value. What is this minimum or maximum value? $\square$ (Simplify your answer.)

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Problem 1070

$f(x)=2 x^{2}-8 x+6$
The quadratic function has a minimum value. The value is $\square$

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Problem 1071

Determine the quadratic function $f$ whose graph is given. The vertex is $(3,-3)$ and the other given point is $(2,-1)$ . $f(x)=$ $\square$ (Simplify your answer.)

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Problem 1072

Determine the quadratic function $f$ whose graph is given. The vertex is $(4,-4)$ and the other given point is $(3,-2)$ . $f(x)=$ $\square$

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Problem 1073

Find values of $k$ such that the line $y=k(-2x+1)$ is tangent to the curve $y=x^2+6$ .

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Problem 1074

Find $k$ such that the line $y=x-k$ is tangent to the curve $k x^{2}-2 x y-4 x-3=0$ .

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Problem 1075

Find the average rate of change of $h(x)=x^{2}-10x$ from $x=-5$ to $x=0$ .

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Problem 1076

Find the average velocity of an object launched with $h(t)=-16 t^{2}+48 t+80$ in the first 2 seconds.

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Problem 1077

Find the $x$ -intercepts of the equation $y=x^{2}+5 x+6$ . Options: a. $-2,3$ b. $-2,-3$ c. $2,-3$ d. $2,3$

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Problem 1078

Factor the polynomial completely or state if it's prime: $4 x^{2}-4 x-24$

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Problem 1079

Solve the equation: $x^{2} = -8x$

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Problem 1080

Factor the equation $x^{2}-10 x+25-y^{2}$ fully.

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Problem 1081

A basketball player shoots from 6 ft high at 45 degrees. Use $h(x)=-\frac{44 x^{2}}{25^{2}}+x+6$ to find height at $x=3$ .

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Problem 1082

이차방정식 $P(x)=0$ 의 두 근 $\alpha, \beta$ 가 주어질 때, $\frac{\alpha+\beta}{\alpha \beta}$ 의 값을 구하시오. (단, $\alpha \neq \beta$ )

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Problem 1083

Find the range of values for $a$ such that the line $y=2x-\frac{a^{2}}{2}$ intersects the curve $y=x^{2}-ax-4$ at two distinct points.

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Problem 1084

If $f(X)=x^{2}$ for $x \in[-2,2]$ , what is the range of $f(X)$ ?

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Problem 1085

Find the range of $f(x)=x^{2}$ for $x \in[-2,2]$ . What values does $f(x)$ take?

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Problem 1086

Find two whole numbers $n$ and $m$ such that $n^2 < 31 < m^2$ . What are these numbers?

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Problem 1087

Express $m$ in terms of $y$ and $x$ from the equation $y=m x^{2}$ .

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Problem 1088

Determine the quadratic function whose graph is given below. -10 (-3,2) 22- -22- (0, -7) 10 X G Points: 0 of 1 The quadratic function which describes the given graph is f(x) = ☐ (Type an expression.)

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Problem 1089

Graph the function $f(x)=(x+5)^{2}-4$ by starting with the graph of $y=x^{2}$ and using transformations (shifting, stretching/compressing, and/or reflecting).
Use the graphing tool to graph the function.
Click to enlarge graph

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Problem 1090

For the quadratic function $f(x)=x^{2}+2 x+1$ , answer parts (a) through ( $f$ ). (a) Find the vertex and the axis of symmetry of the quadratic function, and determine whether the graph is concave up or concave down.
The vertex is $\square$ (Type an ordered pair, using integers or fractions.)

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Problem 1091

For the quadratic function $f(x)=x^{2}+2 x+1$ , answer parts (a) through $(f)$ . (a) Find the vertex and the axis of symmetry of the quadratic function, and determine whether the graph is concave up or concave down.
The vertex is $(-1,0)$ . (Type an ordered pair, using integers or fractions.) What is the equation of the axis of symmetry? The axis of symmetry is $x=-1$ . (Use integers or fractions for any numbers in the equation.) Is the graph concave up or concave down? Concave down Concave up (b) Find the $y$ -intercept and the $x$ -intercepts, if any. Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. The $\bar{x}$ -intercept(s) is/are $\square$ . (Type an integer or a simplified Yaction. Use a comma to separate answers as needed.) B. There are no $x$ -intercepts.

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Problem 1092

$4 x^{2}+9 x-7=2$

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Problem 1093

For the quadratic function $f(x)=x^{2}+2 x+1$ , answer parts (a) through $(f)$ . (a) Find the vertex and the axis of symmetry of the quadratic function, and determine whether the grap
The vertex is $(-1,0)$ . (Type an ordered pair, using integers or fractions.) What is the equation of the axis of symmetry? The axis of symmetry is $x=-1$ . (Use integers or fractions for any numbers in the equation.) Is the graph concave up or concave down? Concave down Concave up (b) Find the $y$ -intercept and the $x$ -intercepts, if any. Select the correct choice below and, if necessary, fi your choice. A. The $x$ -intercept(s) is/are -1 . $\square$ (Type an integer or a simplified fraction. Use a comma to separate answers as needed.) B. There are no $x$ -intercepts.
What is the $y$ -intercept? Select the correct choice below and, if necessary, fill in the answer box to com A. The $y$ -intercept is 1 . $\square$ (Type an integer or a simplifed fraction.) B. There is no y-intercept. (c) Use parts (a) and (b) to graph the function.
Use the graphing tool to graph the function. $\square$ (d) Find the domain and the range of the quadratic function.
The domain of $f$ is $\square$ 7. (Type your answer in interval notation.)

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Problem 1094

For the quadratic function $f(x)=x^{2}+2 x+1$ , answer parts $(a)$ through ( $f$ ). (Type an ordered pair, using integers or fractions.) What is the equation of the axis of symmetry? The axis of symmetry is $x=-1$ . (Use integers or fractions for any numbers in the equation.) Is the graph concave up or concave down? Concave down Concave up (b) Find the $y$ -intercept and the x-intercepts, if any. Select the correct choice below and, if necessary, fill in the answer box to comp your choice. A. The $x$ -intercept(s) is/are -1 . (Type an integer or a simplified fraction. Use a comma to separate answers as needed.) B. There are no x-intercepts.
What is the y-intercept? Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. The $y$ -intercept is 1 . (Type an integer or a simplified fraction.) B. There is no $y$ -intercept. (c) Use parts (a) and (b) to graph the function.
Use the graphing tool to graph the function. - $\square$ (d) Find the domain and the range of the quadratic function.
The domain of $f$ is $(-\infty, \infty)$ . (Type your answer in interval notation.) The range of $f$ is $[0, \infty)$ . (Type your answer in interval notation.) (e) Determine where the quadratic function is increasing and where it is decreasing.
The function is increasing on the interval $\square$ (Type your answer in interval notation.)

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Problem 1095

For the quadratic function $f(x)=x^{2}+2 x+1$ , answer parts (a) through ( $f$ ). (Type an integer or a simplified fraction. Use a comma to separate answers as needed.) B. There are no $x$ -intercepts.
What is the $y$ -intercept? Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. The $y$ -intercept is 1 . (Type an integer or a simplified fraction.) B, There is no $y$ -intercept. (c) Use parts (a) and (b) to graph the function.
Use the graphing tool to graph the function. $\square$ (d) Find the domain and the range of the quadratic function.
The domain of $f$ is $(-\infty, \infty)$ . (Type your answer in interval notation.) The range of $f$ is $[0, \infty)$ . (Type your answer in interval notation.) (e) Determine where the quadratic function is increasing and where it is decreasing.
The function is increasing on the interval $(-1, \infty)$ . (Type your answer in interval notation.) The function is decreasing on the interval $(-\infty,-1)$ . (Type your answer in interval notation.) (f) Determine where $f(x)>0$ and where $f(x)<0$ . Select the correct choice below and fill in the answer box(es) within your choice. (Type your answer in interval notation. Use integers or fractions for any numbers in the expression.) A. $f(x)>0$ on $\square$ and $f(x)<0$ on $\square$ $\square$ B. $f(x)<0$ on $\square$ and $f(x)$ is never positive $\square$ C. $f(x)>0$ on $\square$ and $f(x)$ is never negative

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Problem 1096

For the quadratic function $f(x)=x^{2}+2 x+1$ , answer parts (a) through ( $f$ ).
Is the graph concave up or concave down?
Concave down (Type your answer in interval notation.) (f) Determine where $f(x)>0$ and where $f(x)<0$ . Select the correct cholce below and fill in the answer box(es) within your choice. (Type your answer in interval notation. Use integers or fractions for any numbers in the expression.) A. $f(x)>0$ on $\square$ and $f(x)<0$ on $\square$ B. $f(x)<0$ on 0 and $f(x)$ is never positive C. $f(x)>0$ on $\square$ and $f(x)$ is never negative

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Problem 1097

estion list
For the quadratic function $f(x)=x^{2}+4 x-5$ , answer parts (a) through (f).
Question 1
Question 2
Uestion 3 uestion 4 uestion 5 uestion 6
Iestion 7
Iestion 8 estion 9 estion 10 (a) Find the vertex and the axis of symmetry of the quadratic function, and determine wh
The vertex is $(-2,-9)$ . (Type an ordered pair, using integers or fractions.) What is the equation of the axis of symmetry? The axis of symmetry is $x=-2$ . (Use integers or fractions for any numbers in the equation.) Is the graph concave up or concave down? Concave down Concave up (b) Find the $y$ -intercept and the $x$ -intercepts, if any.
What is the $y$ -intercept? Select the correct choice below and, if necessary, fill in the ansv A. The $y$ -intercept is -5 . (Type an integer or a simplified fraction.) B. There is no $y$ -intercept.
What is the x-intercept? Select the correct choice below and, if necessary, fill in the ans A. The $x$ -intercept(s) is (Type an integer or a simplified fraction. Use a comma to separate answers as n B. There is/are no $x$ -intercept(s). (c) Use parts (a) and (b) to graph the function.
Use the graphing tool to graph the function.

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Problem 1098

For the quadratic function $f(x)=x^{2}+4 x-5$ , answer parts (a) through ( $f$ ). (a) Find the vertex and the axis of symmetry of the quadratic function, and determine whether the graph is concave up or concave down.
The vertex is $(-2,-9)$ . (Type an ordered pair, using integers or fractions.) What is the equation of the axis of symmetry? The axis of symmetry is $x=-2$ . (Use integers or fractions for any numbers in the equation.) Is the graph concave up or concave down? Concave down Concave up (b) Find the $y$ -intercept and the $x$ -intercepts, if any.
What is the $y$ -intercept? Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. The $y$ -intercept is -5 . (Type an integer or a simplified fraction.) B. There is no $y$ -intercept.
What is the x-intercept? Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. The $x$ -intercept(s) is/áre $-5,1$ . (Type an integer or a simplified fraction. Use a comma to separate answers as needed.) B. There is/are no x-intercept(s). (c) Use parts (a) and (b) to graph the function.
Use the graphing tool to graph the function. (d) Find the domain and the range of the quadratic function.
The domain of $f$ is $(-\infty, \infty)$ . (Type your answer in interval notation.) The range of $f$ is $[-9, \infty)$ . (Type your answer in interval notation.) (e) Determine where the quadratic function is increasing and where it is decreasing.
The function is increasing on the interval $\square$ (Type your answer in interval notation.)

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Problem 1099

For the quadratic function $f(x)=x^{2}+4 x-5$ , answer parts (a) through (f). Concave down Concave up (b) Find the $y$ -intercept and the $x$ -intercepts, if any.
What is the $y$ -intercept? Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. The $y$ -intercept is -5 . $\square$ (Type an integer or a simplified fraction.) B. There is no $y$ -intercept.
What is the $x$ -intercept? Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. The $x$ -intercept(s) is/are $-5,1$ . $\square$ (Type an integer or a simplified fraction. Use a comma to separate answers as needed.) B. There is/are no $x$ -intercept(s). (c) Use parts (a) and (b) to graph the function.
Use the graphing tool to graph the function. $\square$ (d) Find the domain and the range of the quadratic function.
The domain of $f$ is $(-\infty, \infty)$ . (Type your answer in interval notation.) The range of $f$ is $[-9, \infty)$ . (Type your answer in interval notation.) (e) Determine where the quadratic function is increasing and where it is decreasing.
The function is increasing on the interval $(-2, \infty)$ . (Type your answer in interval notation.) The function is decreasing on the interval $(-\infty,-2)$ . (Type your answer in interval notation.) (f) Determine where $f(x)>0$ and where $f(x)<0$ . Select the correct choice below and fill in the answer box(es) within your choice. (Type your answer in interval notation. Use integers or fractions for any numbers in the expression.) A. $f(x)>0$ on $\square$ , and $f(x)$ is never negative $\square$ B. $f(x)>0$ on $\square$ , and $f(x)<0$ on $\square$ C. $f(x)<0$ on $\square$ , and $f(x)$ is never positive

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Problem 1100

For the quadratic function $f(x)=x^{2}+4 x-5$ , answer parts (a) through ( $f$ . (Type your answer in interval notation.) (f) Determine where $f(x)>0$ and where $f(x)<0$ . Select the correct choice below and fill in the answer box (es) within your choice. (Type your answer in interval notation. Use integers or fractions for any numbers in the expression.) A. $f(x)>0$ on $\square$ , and $f(x)$ is never negative $\square$ B. $f(x)>0$ on $\square$ , and $f(x)<0$ on $\square$ C. $f(x)<0$ on $\square$ ], and $f(x)$ is never positive

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Quadratics

Problem 1001

Solve the equation −9x2=−8x+8-9 x^{2}=-8 x+8−9x2=−8x+8.

Problem 1002

Factor the expression b2−9b^{2}-9b2−9 completely over the integers.

Problem 1003

Rewrite the expression 2x2−8x+52x^{2}-8x+52x2−8x+5 as a(x−h)2+ka(x-h)^{2}+ka(x−h)2+k.

Problem 1004

How do the signs of bbb and ccc in x2+bx+cx^{2}+b x+cx2+bx+c affect ppp and qqq in (x+p)(x+q)(x+p)(x+q)(x+p)(x+q)?

Problem 1005

Problem 1006

Solve x2=36x^{2}=36x2=36. Which solutions are correct? Select all that apply: x=6x=6x=6, x=362x=36^{2}x=362, x=−6x=-6x=−6, x=18x=18x=18, x=−18x=-18x=−18.

Problem 1007

Solve x2=16x^{2}=16x2=16 and select all correct answers: x=−4x=-4x=−4, x=4x=4x=4, x=−8x=-8x=−8, x=162x=16^{2}x=162, x=8x=8x=8.

Problem 1008

Solve x2=81x^{2}=81x2=81. Which solutions are correct? Select all that apply: x=9x=9x=9, x=−9x=-9x=−9, x=7x=7x=7, x=−7x=-7x=−7.

Problem 1009

Find the solutions for x2=9x^{2}=9x2=9. Select all correct answers: x=18x=18x=18, x=81x=81x=81, x=−81x=-81x=−81, x=−3x=-3x=−3, x=3x=3x=3.

Problem 1010

Solve x2=25x^{2}=25x2=25. Which solutions are correct? Choose all that apply: x=±5x= \pm \sqrt{5}x=±5​, x=25x=25x=25, x=5x=5x=5, x=−25x=-25x=−25, x=−5x=-5x=−5.

Problem 1011

Solve x2=144x^{2}=144x2=144. Which solutions are correct? Choose all that apply: x=72x=72x=72, x=12x=12x=12, x=−72x=-72x=−72, x=11x=11x=11, x=−12x=-12x=−12.

Problem 1012

Find h(6)h(6)h(6) if h(x)=x2−4h(x) = x^{2} - 4h(x)=x2−4.

Problem 1013

Find the yyy-coordinate of the vertex of the parabola ggg given points (-1, 1), (3, 9), (4, 6) and x=2x=2x=2.

Problem 1014

Find the value of kkk for the quadratic function y=f(x)y=f(x)y=f(x) passing through (5,1),(7,k),(9,26)(5,1),(7,k),(9,26)(5,1),(7,k),(9,26) with average rate change of 1.5.

Problem 1015

Find the quadratic equation f(x)f(x)f(x) that matches the points: (−1,10)(-1, 10)(−1,10), (0,14)(0, 14)(0,14), and (1,20)(1, 20)(1,20).

Problem 1016

What transformation changes f(x)=2x2+10f(x)=2x^{2}+10f(x)=2x2+10 to g(x)=8x2+10g(x)=8x^{2}+10g(x)=8x2+10?

Problem 1017

Identify the transformation that changes f(x)=3(x−6)2f(x)=3(x-6)^{2}f(x)=3(x−6)2 into g(x)=3x2+10g(x)=3x^{2}+10g(x)=3x2+10.

Problem 1018

Identify the transformation that changes f(x)=8x2−8f(x)=8 x^{2}-8f(x)=8x2−8 to g(x)=x2−1g(x)=x^{2}-1g(x)=x2−1.

Problem 1019

Identify the transformation that changes f(x)=10x2−5f(x)=10 x^{2}-5f(x)=10x2−5 to g(x)=2x2−1g(x)=2 x^{2}-1g(x)=2x2−1.

Problem 1020

Problem 1021

Expand (2x−3)2(2 x-3)^{2}(2x−3)2. Choose from: 4x2−94 x^{2}-94x2−9, 4x2+94 x^{2}+94x2+9, 2x2−12x+92 x^{2}-12 x+92x2−12x+9, 4x2−12x+94 x^{2}-12 x+94x2−12x+9.

Problem 1022

Find the average rate of change of the function f(x)=x2+6x+10f(x)=x^{2}+6x+10f(x)=x2+6x+10 over the interval [−2,1][-2,1][−2,1].

Problem 1023

Solve by factoring: x2+5x+6=0x^{2}+5x+6=0x2+5x+6=0. Find the roots. Options: −3,−2-3,-2−3,−2; 3,23,23,2; −3,2-3,2−3,2; 3,−23,-23,−2.

Problem 1024

Factor the quadratic x2+14x+45x^{2}+14x+45x2+14x+45. Choose from the options: (x+9)(x+5)(x+9)(x+5)(x+9)(x+5), (x+9)(x−5)(x+9)(x-5)(x+9)(x−5), (x+10)(x+4)(x+10)(x+4)(x+10)(x+4), (x+8)(x+6)(x+8)(x+6)(x+8)(x+6).

Problem 1025

Determine if the function h(x)=x2+1h(x)=x^{2}+1h(x)=x2+1 is even, odd, or neither using algebraic methods.

Problem 1026

A ball's height after ttt seconds is h(t)=144t−16t2h(t)=144t-16t^{2}h(t)=144t−16t2. What does h(2)=224h(2)=224h(2)=224 mean?

Problem 1027

Find the quadratic function h(t)h(t)h(t) for a ball that reaches 16 feet at 1 second and returns to the ground at 2 seconds.

Problem 1028

Factoriza (x+y)2−z2(x+y)^{2}-z^{2}(x+y)2−z2.

Problem 1029

Solve the equation x2+5x+1=0x^{2}+5x+1=0x2+5x+1=0 and round your answers to one decimal place.

Problem 1030

Determine the direction in which the parabola y=−13x2+2y=-\frac{1}{3} x^{2}+2y=−31​x2+2 opens.

Problem 1031

Find the zeros of the equation y=4x2−36y=4x^{2}-36y=4x2−36. List the values of xxx separated by commas.

Problem 1032

Find the end behavior of yyy as x→∞x \to \inftyx→∞ for y=−2x2+4x+2y = -2x^{2} + 4x + 2y=−2x2+4x+2.

Problem 1033

The parabola y=3x2+4y=3 x^{2}+4y=3x2+4 opens upwards.

Problem 1034

Determine the direction in which the parabola x=23y2−3x=\frac{2}{3} y^{2}-3x=32​y2−3 opens.

Problem 1035

Find the value(s) of xxx when y=3y=3y=3 in the equation y=2x2−5y=2x^2-5y=2x2−5.

Problem 1036

Find where the polynomial y=x2+3x+2y=x^{2}+3x+2y=x2+3x+2 intersects the yyy-axis.

Problem 1037

Find the xxx-values where y=x2+5x+6y = x^{2} + 5x + 6y=x2+5x+6 intersects the xxx-axis. (List answers separated by commas.)

Problem 1038

Find the points where the polynomial y=x2−4x+3y=x^{2}-4 x+3y=x2−4x+3 intersects the x\mathrm{x}x-axis.

Problem 1039

Use the graph of the quadratic function fff to determine the solution. (a) Solve f(x)>0f(x)>0f(x)>0. (b) Solve f(x)≤0f(x) \leq 0f(x)≤0. (a) The solution to f(x)>0f(x)>0f(x)>0 is □\square□ (Type your answer in interval notation.)

Problem 1040

4. Discriminant and solutions of a quadratic equation from a graphGiven the discriminant, match it to its graph, then give the reason for your selection

Problem 1041

Solve the equation $-9 x^{2}=-8 x+8$ .

Factor the expression $b^{2}-9$ completely over the integers.

Rewrite the expression $2x^{2}-8x+5$ as $a(x-h)^{2}+k$ .

How do the signs of $b$ and $c$ in $x^{2}+b x+c$ affect $p$ and $q$ in $(x+p)(x+q)$ ?

Solve $x^{2}=36$ . Which solutions are correct? Select all that apply: $x=6$ , $x=36^{2}$ , $x=-6$ , $x=18$ , $x=-18$ .

Solve $x^{2}=16$ and select all correct answers: $x=-4$ , $x=4$ , $x=-8$ , $x=16^{2}$ , $x=8$ .

Solve $x^{2}=81$ . Which solutions are correct? Select all that apply: $x=9$ , $x=-9$ , $x=7$ , $x=-7$ .

Find the solutions for $x^{2}=9$ . Select all correct answers: $x=18$ , $x=81$ , $x=-81$ , $x=-3$ , $x=3$ .

Solve $x^{2}=25$ . Which solutions are correct? Choose all that apply: $x= \pm \sqrt{5}$ , $x=25$ , $x=5$ , $x=-25$ , $x=-5$ .

Solve $x^{2}=144$ . Which solutions are correct? Choose all that apply: $x=72$ , $x=12$ , $x=-72$ , $x=11$ , $x=-12$ .

Find $h(6)$ if $h(x) = x^{2} - 4$ .

Find the $y$ -coordinate of the vertex of the parabola $g$ given points (-1, 1), (3, 9), (4, 6) and $x=2$ .

Find the value of $k$ for the quadratic function $y=f(x)$ passing through $(5,1),(7,k),(9,26)$ with average rate change of 1.5.

Find the quadratic equation $f(x)$ that matches the points: $(-1, 10)$ , $(0, 14)$ , and $(1, 20)$ .

What transformation changes $f(x)=2x^{2}+10$ to $g(x)=8x^{2}+10$ ?

Identify the transformation that changes $f(x)=3(x-6)^{2}$ into $g(x)=3x^{2}+10$ .

Identify the transformation that changes $f(x)=8 x^{2}-8$ to $g(x)=x^{2}-1$ .

Identify the transformation that changes $f(x)=10 x^{2}-5$ to $g(x)=2 x^{2}-1$ .

Expand $(2 x-3)^{2}$ . Choose from: $4 x^{2}-9$ , $4 x^{2}+9$ , $2 x^{2}-12 x+9$ , $4 x^{2}-12 x+9$ .

Find the average rate of change of the function $f(x)=x^{2}+6x+10$ over the interval $[-2,1]$ .

Solve by factoring: $x^{2}+5x+6=0$ . Find the roots. Options: $-3,-2$ ; $3,2$ ; $-3,2$ ; $3,-2$ .

Factor the quadratic $x^{2}+14x+45$ . Choose from the options: $(x+9)(x+5)$ , $(x+9)(x-5)$ , $(x+10)(x+4)$ , $(x+8)(x+6)$ .

Determine if the function $h(x)=x^{2}+1$ is even, odd, or neither using algebraic methods.

A ball's height after $t$ seconds is $h(t)=144t-16t^{2}$ . What does $h(2)=224$ mean?

Find the quadratic function $h(t)$ for a ball that reaches 16 feet at 1 second and returns to the ground at 2 seconds.

Factoriza $(x+y)^{2}-z^{2}$ .

Solve the equation $x^{2}+5x+1=0$ and round your answers to one decimal place.

Determine the direction in which the parabola $y=-\frac{1}{3} x^{2}+2$ opens.

Find the zeros of the equation $y=4x^{2}-36$ . List the values of $x$ separated by commas.

Find the end behavior of $y$ as $x \to \infty$ for $y = -2x^{2} + 4x + 2$ .

The parabola $y=3 x^{2}+4$ opens upwards.

Determine the direction in which the parabola $x=\frac{2}{3} y^{2}-3$ opens.

Find the value(s) of $x$ when $y=3$ in the equation $y=2x^2-5$ .

Find where the polynomial $y=x^{2}+3x+2$ intersects the $y$ -axis.

Find the $x$ -values where $y = x^{2} + 5x + 6$ intersects the $x$ -axis. (List answers separated by commas.)

Find the points where the polynomial $y=x^{2}-4 x+3$ intersects the $\mathrm{x}$ -axis.

Use the graph of the quadratic function $f$ to determine the solution. (a) Solve $f(x)>0$ . (b) Solve $f(x) \leq 0$ . (a) The solution to $f(x)>0$ is $\square$ (Type your answer in interval notation.)

4. Discriminant and solutions of a quadratic equation from a graph
Given the discriminant, match it to its graph, then give the reason for your selection

Given the function defined by $g(x)=-x^{2}+3 x+3$ , find $g(-2)$ . Simplify. $g(-2)=$ $\square$

Given the function defined by $g(x)=3 x^{2}-7 x+3$ , find $g(-2 x)$ . Express the answer in simplest form. $g(-2 x)=$

Solve the polynomial inequality and graph the solution set on a real number line. Express the solution set in interval notation. $x^{2}+8 x+15>0$

Factor completely. $c^{2}-12 c+36$
Select the correct choice below and fill in any answer boxes within your choice. A. $c^{2}-12 c+36=$ $\square$ B. The expression is prime.

Factor completely. $r^{2}+25$
Select the correct choice below and fill in any answer boxes within your choice. A. The answer is $\square$ . B. The expression is prime.

Solve the quadratic equation by completing the square. $x^{2}+2 x=15$
The solution set is $\square$ \}. (Type an integer or a simplified fraction. Use a comma to separate answers as needed.)

Solve using the quadratic formula. $9 r^{2}+6 r+1=0$

Solve for $x$ and graph the solution. $-34 x^{2}-13 x+46 \leq-33 x^{2}-13 x+37$
Plot the endpoints. Select an endpoint to change it from closed to open. Select the middle of a segment, ray, or line to delete it. Submit

Solve for $x$ and graph the solution. $x^{2}-7>4 x-2$
Plot the endpoints. Select an endpoint to change it from closed to open. Select the middle of a segment, ray, or line to delete it. Submit

Question 30 of 60
Use the quadratic formula to solve the equation. $5 x^{2}-2 x=1$
The solution set is $\square$ B. (Simplify your answer. Type an exact answer, using radicals and $i^{\prime}$ as needed. Use integers or fractions for ar

8. For the function $f(x)=2(x-3)^{2}+2$ , determine the location of the vertex and the $\mathbf{x}$ and y -intercepts.

a.) Calculate the discriminant by hand and state the rumber and type of solutions to the equation $x^{2}+2 x=2$

Solve $x^{2}+2 x=2$ , using the quadratic formula (show as much work as possible). Remember the quadratic formula is: $x=\frac{-b \pm \sqrt{b^{2}-4 a c}}{2 a}$ .

Find the minimum value of the parabola $y=x^{2}+4 x+1$
Simplify your answer and write it as a proper fraction, improper fraction, or integer. $\square$

Factor the equation $y = x^2 + 5x + 1$ .

$\qquad$ 14 $\qquad$ $\qquad$
7. Simplifying tho quadratic formula complete the next otrepe tio fimal the collutinst Fin) simplym the malicul if nerind Th) Simplify the equation if encthet

Simplify. (a) $(4-\sqrt{5})^{2}$ $\square$ (b) $(10+2 \sqrt{7})^{2}$ $\square$

$f(x)=-3 x^{2}+6 x$
The quadratic function has a $\square$ value.

$f(x)=3 x^{2}+24 x-3$
Does the quadratic function $f$ have a minimum value or a maximum value? The function $f$ has a maximum value. The function $f$ has a minimum value.

$f(x)=3 x^{2}+24 x-3$
Does the quadratic function $f$ have a minimum value or a maximum value? The function $f$ has a maximum value. The function $f$ has a minimum value. What is this minimum or maximum value? $\square$ (Simplify your answer.)

$f(x)=2 x^{2}-8 x+6$
The quadratic function has a minimum value. The value is $\square$

Determine the quadratic function $f$ whose graph is given. The vertex is $(3,-3)$ and the other given point is $(2,-1)$ . $f(x)=$ $\square$ (Simplify your answer.)

Determine the quadratic function $f$ whose graph is given. The vertex is $(4,-4)$ and the other given point is $(3,-2)$ . $f(x)=$ $\square$

Find values of $k$ such that the line $y=k(-2x+1)$ is tangent to the curve $y=x^2+6$ .

Find $k$ such that the line $y=x-k$ is tangent to the curve $k x^{2}-2 x y-4 x-3=0$ .