Browse Quadratics problems Studdy Solved!

Problem 501

Identify the vertex and the axis of symmetry for the function. $g(x)=(x-44)^{2}$
The vertex of the function is $\square$ (Type an ordered pair.)

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Problem 502

Solve for $y$ . $(y-2)^{2}=2 y^{2}-12 y+16$
If there is more than one solution, separate them with commas.

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Problem 503

Rewrite without parentheses and simplify. $(5 y+6 v)^{2}$

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Problem 504

i) Faktorkan selengkapnya Factorise completely $6 m^{2}-7 m-20$
Jawapan / Answer.

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Problem 505

$(x+5)^{2}-16=0$

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Problem 506

Question Watch Video
Solve for all values of $x$ by factoring. $x^{2}-4 x-59=-4 x+5$
Answer Attempt 1 out of 2

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Problem 507

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Solve for all values of $x$ by factoring. $x^{2}+10 x-40=4 x$

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Problem 508

Solve the quadratic by factoring. $3 x^{2}+12 x=7 x+2$

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Problem 509

1) (5 marks)
Multiple Choice Circle the appropriate answer.
1. Which of the following is true about the parabola for the function $(x)-3(x-4)^{2}+5$ ? a. The $y$ -intercept is 5 . c. The axis of symmetry is $x=-4$ . b. The vertex is $(4,5)$ . d. The parabola opens up.
2. The points $(-3,5)$ and $(9,5)$ are the same distance from the vertex of their parabola. What is the equation for the axis of symmetry of the parabola? a. $x=5$ b. $x=0$ c. $\quad x=-3$ d. $\quad x=3$
3. What is the maximum value for the function $(x)-8(x+6)^{2}-12$ ? a. $\quad-8$ b. 6 c. -12
4. Given $f(x)=-(x+4)^{2}-7$ , what is true for vertex point? d. none of these a. $\operatorname{Max},(4,-7)$ c. $\operatorname{Min},(4,-7)$ b. Max, $(-4,-7)$ d. $\operatorname{Min} .(-4,-7)$
5. How many zeros are in the solution to the function $f(x)=x^{2}-7 x-2$ ? a. 0 b. 1 c. 2 d. 3

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Problem 510

Question Watch $v$
Solve the quadratic by factoring. $5 x^{2}-20 x+14=2 x+6$

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Problem 511

Question Watch Video
Factor completely. $4 x^{2}-64 x+252$
Answer Attempt 1 out of 2

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Problem 512

What are the solutions to $2 x^{2}+8 x+4=0$ ? $x=-6 \pm \sqrt{2}$ $x=-6 \pm 6 \sqrt{2}$ $x=-2 \pm \sqrt{2}$ $x=-2 \pm \frac{\sqrt{30}}{3}$

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Problem 513

Fill in the info below, and graph on your own paper. Then graph the parabola on the axes below by first clicking on the vertex, and then on another point close to the vertex that fits on the axes. You may not be able to click on an x or y intercept. $y=-x^{2}-10 x-24$
1. State whether the parabola opens up or down?
UpO Down
2. State the vertex as an ordered pair: $\square$
3. State the $y$ -intercept as an ordered pair: $\square$
4. Write the Equation of the Axis of Symmetry: $\square$
5. Click on the vertex and then another point of the parabola that fits on the axes below. Clear All Draw:

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Problem 514

Graph $f(x)=-\frac{1}{2} x^{2}-x-\frac{3}{2}$ using the Quadratic Formula. State both coordinates of the $x$ -intercept, $y$ -intercept, and vertex.

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Problem 515

$f(x)=5 x^{2}+30 x+42$
In vertex form $f(x)=a(x-h)^{2}+k$ the value of $a=$ $\square$ the value of $h=$ $\square$ and the value of $k=$ $\square$

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Problem 516

PRACTISING
4. Determine the maximum or minimum value. Use at least two different $\mathbf{K}$ methods. a) $y=x^{2}-4 x-1$ d) $y=-3 x^{2}-12 x+15$ b) $f(x)=x^{2}-8 x+12$ e) $y=3 x(x-2)+5$ c) $y=2 x^{2}+12 x$ f) $g(x)=-2(x+1)^{2}-5$

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Problem 517

Select the quadratic equation in vertex form AND standard form. $(11 x+4)^{2}$ $x^{2}+\frac{8}{11} x+\frac{16}{121}$

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Problem 518

4. Describe the transformations that are applied to the graph of $y=x^{2}$ to obtain the graph of each quadratic relation. a) $y=x^{2}+5$ c) $y=-3 x^{2}$ e) $y=\frac{1}{2} x^{2}$ b) $y=(x-3)^{2}$ d) $y=(x+7)^{2}$ f) $y=(x+6)^{2}+12$

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Problem 519

5.3.1 \#14 18
Write the quadratic function with a vertex of $(2,-5)$ that also goes through $(1,-2)$ in standard form.
The equation of the quadratic in standard form is $f(x)=$ [ Select] $\square$ $x^{2}+$ $\square$ [ Select] $x+$ [Select] $\square$

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Problem 520

Solve for $w$ . $w^{2}-9 w+14=0$
If there is more than one solution, separate them wit If there is no solution, click on "No solution."

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Problem 521

Question Watch Video Show Examples
Write two numbers that multiply to the value on top and add to the value on bottom.

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Problem 522

Question Watch Video Show Examples
Write two numbers that multiply to the value on top and add to the value on bottom.

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Problem 523

The functions $f$ and $g$ are defined as follows. $f(x)=x^{2}-2 x-6 \text { and } g(x)=\frac{5 x-1}{9 x-4}$
Find $f(x+7)$ and $g\left(\frac{x}{2}\right)$ . Write your answers without parentheses and simplify them as much as possible. $\begin{array}{l} f(x+7)=\square \\ g\left(\frac{x}{2}\right)=\square \end{array}$

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Problem 524

Submit Question Question 7 $0.5 / 1 \mathrm{pt}$ 2 98 Details
NASA launches a rocket at $t=0$ seconds. Its height, in meters above sea-level, as a function of time is given by $h(t)=-4.9 t^{2}+271 t+276$ . 23
Assuming that the rocket will splash down into the ocean, at what time does splashdown occur?
The rocket splashes down after $\square$ seconds.
How high above sea-level does the rocket get at its peak? The rocket peaks at $\square$ meters above sea-level. Question Help: Video 1 Video 2 Calculator Submit Question Question 8 $1 / 1 \mathrm{pt}$ 1 99 Details

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Problem 525

Solve by using the quadratic formula: $6 x^{2}+3 x-7=0$ .

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Problem 526

$3=x^{2}+2 x$

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Problem 527

2. A firework is launched upward at an initial velocity of $49 \mathrm{~m} / \mathrm{s}$ , from a height of 1.5 m above the ground. The height of the firework, in metres, after $t$ seconds, is modelled by the equation $h=-4.9 t^{2}+49 t+1.5$ . a) What is the maximum height of the firework above the ground? b) Over what time interval is the height of the firework greater than 100 m above the ground? Round to the nearest hundredth of a second.

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Problem 528

0. Determine and interpret the zeros in terms of the context. A company's profit in the years since 2000 is modeled by the equation: $C(x)=-2 x^{2}+20 x+48$ .

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Problem 529

1. Without the use of your calculator, evaluate each of the following quadratic functions for the specified input values. (a) $g(x)=x^{2}-9$ (b) $f(x)=-2 x^{2}+8 x$ (c) $h(x)=x^{2}-2 x+6$ $\begin{array}{lll} g(5)= & f(3)= & h(0)= \\ g(-3)= & f(-1)= & h(-2)= \end{array}$

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Problem 530

2. Which of the following represents the $y$ -intercept of the graph of the quadratic function $y=2 x^{2}-7 x+9$ ? (Recall, that the $y$ -intercept of a graph always occurs when $x=0$ .) (1) 7 (3) -7 (2) 2 (4) 9

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Problem 531

8. The height of a ball thrown vertically upward from a rooftop is modelled by $h(t)=-5 t^{2}+20 t+50$ , where $h(t)$ is the ball's height above the ground, in metres, at time iseconds after the throw. a) Determine the maximum height of the ball. b) How long does it take for the ball to reach its maximum height? c) How high is the rooftop?

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Problem 532

Use the following information to answer the question.
If the equation for the above function is written in the form $y=a x^{2}+b x+c$ , the value of $a$ is
Select one: a. either positive or negative b. negative c. positive d. dependent on the value of $c$

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Problem 533

Graph the functions on the same coordinate plane. $\begin{array}{l} f(x)=-2 x \\ g(x)=x^{2}-3 \end{array}$
What are the solutions to the equation $f(x)=g(x)$ ? Select each correct answer. There are two.
Select 2 correct answer(s)
1 -3 -2 0

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Problem 534

Solve for a. $5 a^{2}=980$
Select both solutions.
Select 2 correct answer(s) -196 -14 196 14

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Problem 535

$x^{2}+4 y^{2}-6 x+16 y+21=0$

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Problem 536

4. The graph of $f(x)=4 x^{2}+3 x-5$ is transformed into the graph of $g(x)=-f(-x)$ . The equation representing $g(x)$ is A. $g(x)=4 x^{2}+3 x+5$ B. $g(x)=4 x^{2}+3 x-5$ C. $g(x)=-4 x^{2}+3 x+5$ D. $g(x)=-4 x^{2}-3 x-5$

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Problem 537

6+ y = (x+ (x + 1)(x-5) 2 4+ -3-2 -1 0 2 3 4 5

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Problem 538

Factor the equation completely. $y^{2}+3 y-28$
Factored Form $\square$

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Problem 539

2. A rectangle has dimensions $x+10$ $2 \mathrm{x}-3$ , where x is in centimetres. Tir area of the rectangle is $54 \mathrm{~cm}^{2}$ . b) What is the value of $x$ ? $2 x^{2}-17 x-84=0$

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Problem 540

2 Etudier le signe de chacun des trinômes suivants après avoir, si nécessaire, déterminé ses racines. $5^{\circ} f(x)=4 x^{2}-16 x+16$ $6^{\circ} f(x)=(3 x-7)(-x+2)$ $\mathbf{8}^{\circ} f(x)=-x^{2}-8$ $9^{\circ} f(x)=(2 x-1)^{2}+16$

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Problem 541

Investigate this question by building rectangles with algebra tiles for the following expressions. For each one, write the area as a sum and as a product. If you cannot build a rectangle, be prepared to convince the class that no rectangle exists (and thus the expression cannot be factored). a. $2 x^{2}+7 x+6$ b. $6 x^{2}+7 x+2$ c. $x^{2}+4 x+1$ d. $2 x y+6 x+y^{2}+3 y$

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Problem 542

3. Which equation has imaginary roots? (1) $x^{2}-1=0$ (2) $x^{2}-2=0$ (3) $x^{2}+x+1=0$ (4) $x^{2}-x-1=0$

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Problem 543

2.6 Indicate the zeros of a function algebraicany.
The zeros of a function are the same as the $x$ -intercepts! (it's where $y=0$ ) $f(x)=0$
Directions: Find the zeros for each of the following equations.
1. $f(x)=4 x^{2}+20 x$
2. $f(x)=x^{2}+2 x-3$
3. $f(x)=5 x^{2}-5 x-150$

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Problem 544

7.2 Determine the real solution(s) (if they exist) of the following quadratic equations (a) $x^{2}+2 x+2=0$ (b) $9 x^{2}-12 x-21=0$ (c) $4 x^{2}-20 x+25=0$ (+) $x^{2}=14 x-50$ (+) On August 7th, the temperature in Klagenfurt was 15 degree Celsius at 6 am and 29 degree Celsius at 1 pm . What was the average temperature gradient (in degree Celsius per hour) during that morning?

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Problem 545

Exercise 1. Express the following in Big- $\Omega$ , Big-O, or Big-Theta notation as appropriate. (a) $n^{2} \leq 3 n(n-2) \leq 4 n^{2}$ , for every integer $n \geq 3$ . (b) $\frac{1}{2} n^{2} \leq \frac{n(3 n-2)}{2}$ , for every integer $n \geq 3$ (c) $0 \leq \frac{n(3 n-2)}{2} \leq n^{2}$ , for every integer $n \geq 2$ .

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Problem 546

Describe the transformation from the parent function. (Mark all that apply) $y=-(x+3)^{2}+2$ Reflected across the $y$ -axis Shifted up 2 units Shifted right 3 units Vertex is $(-3,2)$ Shifted left 3 units Shifted up 3 units Reflected across the x-aris

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Problem 547

Sketch the graph of each inequality. 4) $y \leq-x^{2}+8 x-12$ A) C) B) D)

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Problem 548

789074 $: 3$ 90
Determine the domain and range of the quadratic function shown on the graph. Select two answers.
Select all correct options
$\mathrm{D}: \mathrm{x} \leq-1$ $R: y \leq-1$ D: all real numbers R: all real numbers

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Problem 549

How many solutions can a quadratic have?
1,2, or 3 none, 1, or 2 none or 2 1 or 2

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Problem 550

The graph below represents the path of a squirrel traveling up and down a tree over time.
The position of the squirrel can be calculated using the function $p(t)=a t^{2}+b t+c$ . What is the value of $a$ ? $\square$ What is the value of $b$ ? $\square$ What is the value of $c$ ? $\square$

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Problem 551

Applications | Rapididentity Course Modules: Algebra: Conce Launch Meeting-Zoom Playing a Game - Quivizy https://quizizzcom/join/game/U2FsdGVkX18RUsp8m9SUr9hPqgHgdho3zOM3KeM2mqmPjgkgnHyNTvL900\%252B1bG8MdWa7hL\%252B52VW... 120 789074
Identify the roots of the quadratic. $x=\{-1,3\} \quad x=\{-3\} \quad x=\{1,-4\} \quad x=\{1\}$

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Problem 552

2. Complete the square to find the standard form equatio of the ellipse. $9 x^{2}-54 x+64 y^{2}+512 y+529=0$ $\frac{(x-3)^{2}}{64}+\frac{(y+4)^{2}}{9}=1$ $(x-3)^{2} 64+\frac{(y+4)^{2}}{9}=1$ $\frac{(x-3)^{2}}{64}+\frac{(-4-y)^{2}}{9}=1$ $\frac{(x-3)^{2}}{64}+\frac{(-4-y)^{2}}{27}=1$

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Problem 553

Find all $y$ -intercepts and $x$ -intercepts of the graph of the function. $f(x)=2 x^{2}-15 x+18$
If there is more than one answer, separate them with commas. Click on "None" if applicable.

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Problem 554

$12 x^{2}+10 x-6=-26 x+15$

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Problem 555

\%kuta Software - Infinite Algebra 1 Factoring Trinomials $(a>1)$ Factor each completely. 1) $3 p^{2}-2 p-5$

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Problem 556

Name: $\qquad$ D.
10. Factor this polynomial: $6 x^{2}-13 x-28$
A $(2 x+7)(3 x+4)$ C $(2 x+7)(3 x-4)$
18. $(2 x-7)(3 x-4)$ (D) $(2 x-7)(3 x+4)$

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Problem 557

Complete the square for $h(x)=5 x^{2}+20 x-60$ $\begin{array}{l} x=-2 \\ h(x)=5 x^{2}+2 \\ h(-2)=-80 \\ (-2,-80) \end{array}$

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Problem 558

Solve for x . $\begin{array}{c} 4 x^{2}+4 x+1=0 \\ x=-\frac{[?]}{} \end{array}$

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Problem 559

The graph of a function $g$ is shown below. Find $g(-2)$ and find one value of $x$ for which $g(x)=-5$ . (a) $g(-2)=$ $\square$ (b) One value of $x$ for which $g(x)=-5: 0$

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Problem 560

Which type of conic is represented by the equation below? $x=-3 y^{2}+30 y-80$
This is an equation of a parabola. Write the equation of this conic section in conic form.

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Problem 561

Graph the function. $1 / 5$ $h(x)=-\frac{1}{2} x^{2}$
Plot five points on the graph of the function: one point with $x=0$ , two points with negative $x$ -values, and two points with positive $x$ -values. Then click on the graph-a-function button.

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Problem 562

Factor fully, if possible. a) $x^{2}+7 x+12$

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Problem 563

Question Whatan Vifies
Write two numbers that multiply to the value on top and add to the value ne bretloe

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Problem 564

$y=-2 x^{2}+24 x+5$
Convert to vertex form. $y=-2(x-6)^{2}+77 \quad y=-2(x+6)^{2}+77$ $y=-2(x-12)^{2}+77$ $y=-2(x+12)^{2}+77$ Makenzie Armstrong

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Problem 565

Graph the function using its vertex, axis of symmetry, and intercepts. $f(x)=-x^{2}+6 x-8$

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Problem 566

Convert $f(x)=3 x^{2}+6 x-5$ to vertex form. $f(x)=3(x+2)^{2}-8$ $f(x)=3(x-1)^{2}-8$ $f(x)=3(x-2)^{2}-8$ $f(x)=3(x+1)^{2}-8$ Makenzie Armstrong

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Problem 567

$\begin{array}{l} g(x)=x^{2}+6 x \\ h(x)=x^{2}-1 \end{array}$
Write $g(h(x))$ as an expression in terms of $x$ . $g(h(x))=\square \quad 7$

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Problem 568

Fill in the blanks Enter intercepts as ordered pairs, aka points. Then Graph the parabola given in standard form. You ony need to graph the vertex and one other point.
Standard Form: $f(x)=-x^{2}-4 x$
1. Does the parabola open up or down? O Up Down
2. Vertex $(x, y)=$ $\square$
3. $y$ -intercept $(x, y))=$ $\square$
4. Equation of the Axis of Symmetry: $\square$ Clear mill Draw: $\square$

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Problem 569

What are the solutions to (2 Points) $2 x^{2}+x-3$ 1 $3,-\frac{1}{2}$ $-1, \frac{3}{2}$ $1,-\frac{3}{2}$

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Problem 570

5 Numeric 1 point
Enter a decimal approximation of the rightmost x-intercept of $f(x)=x^{2}+4 x-1$ . Must be after the decimal point.)

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Problem 571

11) $a^{2}+10 a+21$ 12) $n^{2}-11 n+24$ (a) (a
1 $(n)(n$ ) 13) $x^{2}-2 x-15$ $(x)$ 14) $k^{2}-2 k-48$ 15) $x^{2}-5 x-24$ 16) $x^{2}+13 x+40$ $(x)$ $(x)$ ) 17) $u^{2}+5 u v+4 v^{2}$ (u) $u$ ) 18) $x^{2}+6 x y+5 y^{2}$ $\int x$ $\gamma$ 19) $5 x^{2}-70 x+225$
1 20) $6 x^{2}+30 x+36$ $(x)$

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Problem 572

3. Given $f(x)=-3(x-4)^{2}+6$ , determine the following KEY features. $\mathrm{a}=\underline{-2}, \mathrm{~h}=4, \mathrm{k}=6$ \begin{tabular}{|llllll|} \hline OPTIONS & -3 & 3 & -4 & 4 & 6 \\ \hline \end{tabular}
Vertex: $\qquad$ \begin{tabular}{|lllll|} \hline OPTIONS & $(4,6)$ & $(-4,-6)$ & $(4,6)$ & $(-4,6)$ \\ \hline \end{tabular}
Axis of Symmetry: $\qquad$ \begin{tabular}{|llll|} \hline OPTIONS $\quad x=4)(x-2$ & $x=4$ \\ \hline \end{tabular} Vertical Stretch (Narrow)/ Vertical Compression (Wide) / Neither: $\qquad$ \begin{tabular}{|llll|} \hline OPTIONS & Stretch & Compression & Neither \\ \hline \end{tabular}
Horizontal Shift: $\qquad$
Vertical Shift: $\qquad$ \begin{tabular}{|lllll|} \hline OPTIONS & Left 4 & Right 4 & Left 6 & Right 6 \\ \hline OPTIONS & Up 4 & Down 4 & Up 6 & Down 6 \\ \hline \end{tabular}
Direction of Opening: $\qquad$ OPTIONS Up Down
Maximum or Minimum: $\qquad$ OPTIONS Minimum Maximum
4. Given $f(x)=x^{2}+2 x-4$ , determine the following KEY features.
Vertex: $\qquad$
Domain: $\qquad$ Interval of Increase: $\qquad$
Range: $\qquad$ Interval of Decrease: $\qquad$

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Problem 573

-31 $-9$ $\frac{1}{31}$ $\frac{1}{9}$

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Problem 574

4070660/quizzes/12071068/take
A baseball is thrown in a parabolic arc. It's position above the ground at a given point in time can be represented by the quadratic function $p(t)=\frac{1}{2} g t^{2}+v_{0} t+p_{0}$ , where $t \geq 0, g$ is $-32 \mathrm{ft} / \mathrm{sec}^{2}, v_{0}$ is initial velocity, and $p_{0}$ is its initial position above the ground. Assume the ball was thrown straight up at $40 \mathrm{ft} / \mathrm{sec}$ when it was 5 ft above the ground.
What is the value for $v_{0}$ in the equation for $p(t)$ ? $40 \mid$
The vertex for $p(t)$ will be in the form $\left(\frac{A}{B}, C\right)$ based on the given information. Type the numerical values for $A, B$ , and $C$ below. $\begin{array}{l} A=\square \\ B=\square \\ C=\square \end{array}$
How high did the ball go based on the above information? (Type the number, do not include units in your answer)

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Problem 575

Question 1
The image below is a geometric representation of Completing the Square.
Which of the following expressions correctly describes Completing the Square? $x^{2}+a+\left(\frac{a}{2}\right)^{2}$ $x^{2}+2 a x+a^{2}$ $x^{2}+a x+a^{2}$ $x^{2}+a x+\left(\frac{a}{2}\right)^{2}$

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Problem 576

2. Solve the equation by completing the square $x^{2}-12 x+2=-9$

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Problem 577

5. Find the solutions to the following equation $(x+3)^{2}=-36$

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Problem 578

Consider the function $f(x)=-2 x^{2}-12 x+10$ .
For $f(x)$ , the vertex is a maximum value minimum value

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Problem 579

6. $f(x)=-x^{2}+6 x-4$ a. $f(-3)$ b. $f(-1)$ c. $f(5)$

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Problem 580

AY STOP
What is the range of $y=(x-5)^{2}-15 ?$ (A) All real numbers that are greater than or equal to -15 . (B) All real numbers that are greater than or equal to 0 and less than or equal to 30 . (C) All real numbers that are greater than or equal to 0 and less than or equal to 0 -15. (D) All real numbers that are less than or equal to -15 . Search

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Problem 581

On the last item, you showed your reasoning in solving the three equations below by either completing the square or using the quadratic formula (using each approach at least once). Enter your solutions to each equation in the boxes provided. (The order in which you enter your solutions does not matter). a. $x^{2}-12 x=-20$ b. $2 x^{2}+4 x+10=0$ c. $4 x^{2}-5 x-6=0$ $x=10.47$ $x=$ $\square$ $x=$ $\square$ or or or $x=1.52$ $x=$ $\square$ $x=$ $\square$ Scientific Calculator

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Problem 582

Pear Assessment: Home Pear Assessment: Laredo ISD app.edulastic.com/student/assessment/6734d9b55ad2f30008a0f2eb/class/66c2a86d745336dc4296cfb Pool \begin{tabular}{|c|c|} \hline Time, $x$ (seconds) & \begin{tabular}{c} Depth of Person from \\ Surface of Water, $d(x)$ (feet) \end{tabular} \\ \hline 1 & -2.85 \\ \hline 4 & -8.28 \\ \hline 6 & -9.3 \\ \hline 8.5 & -7.65 \\ \hline 10 & -5.1 \\ \hline 11.5 & -1.38 \\ \hline \end{tabular}
Which function best models the data? A) $d(x)=0.05 x^{2}+0.74 x$ (B) $d(x)=0.05 x^{2}+0.74 x+9.17$ (C) $d(x)=0.26 x^{2}-3.11 x$ (D) $d(x)=0.26 x^{2}-3.11 x+1$ Search

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Problem 583

\begin{tabular}{|c|c|} \hline $x$ & $f(x)$ \\ \hline-1 & -6 \\ \hline 0 & -3 \\ \hline 1 & -2 \\ \hline 2 & -3 \\ \hline 3 & -6 \\ \hline \end{tabular} (A) $f(x)=-x^{2}+2 x-3$ (B) $f(x)=x^{2}+2 x+3$ (C) $f(x)=-x^{2}-2 x-3$

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Problem 584

11. Given the function $f(x)=-2 x^{2}+3 x$ find the value of $\frac{\boldsymbol{f}(\boldsymbol{a}+\boldsymbol{h})-\boldsymbol{f}(\boldsymbol{a})}{\boldsymbol{h}}$ .

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Problem 585

$f(x)=2 x^{2}-x-1$ (a) Is the point $(-2,9)$ on the graph of $f$ ? (b) If $x=2$ , what is $f(x)$ ? What point is on the graph of $f$ ? (c) If $f(x)=-1$ , what is $x$ ? What point(s) is/are on the graph of $f$ ? (d) What is the domain of $f$ ? (e) List the $x$ -intercept(s), if any, of the graph of f . (f) List the $y$ -intercept, if there is one, of the graph of f .

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Problem 586

Period $\qquad$ Date $\qquad$ Use the given equation to fill in the missing values in each table. Graph the ordered pairs.
1. $y=x^{2}-3$ \begin{tabular}{|c|c|} \hline $x$ & $y$ \\ \hline-2 & \\ \hline-1 & \\ \hline 0 & \\ \hline 1 & \\ \hline 2 & \\ \hline \end{tabular}
2. $y=2 x-5$ \begin{tabular}{|c|c|} \hline $x$ & $y$ \\ \hline-2 & \\ \hline-1 & \\ \hline 0 & \\ \hline 1 & \\ \hline 2 & \\ \hline \end{tabular}
3. $y=2^{x}$ \begin{tabular}{|c|c|} \hline $x$ & $y$ \\ \hline-2 & \\ \hline-1 & \\ \hline 0 & \\ \hline 1 & \\ \hline 2 & \\ \hline \end{tabular}
TYPE: $\qquad$ TYPE: $\qquad$ TYPE: $\qquad$ Determine if each graph, table or equation is linear or non-linear. If it is non-linear, identify the type of graph (quadratic, exponential or inverse variation). 4. \begin{tabular}{|c|c|} \hline $x$ & $y$ \\ \hline-2 & 4 \\ \hline-1 & 1 \\ \hline 0 & 0 \\ \hline 1 & 1 \\ \hline 2 & 4 \\ \hline \end{tabular} 7. 5.
8. $y=\frac{1}{x}$ 9. \begin{tabular}{|c|c|} \hline $x$ & $y$ \\ \hline-2 & 5 \\ \hline-1 & 8 \\ \hline 0 & 11 \\ \hline 1 & 14 \\ \hline 2 & 17 \\ \hline \end{tabular}

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Problem 587

Answer the questions about the following function. $f(x)=2 x^{2}-x-1$ (a) Is the point $(-2,9)$ on the graph of $f$ ? (b) If $x=2$ , what is $f(x)$ ? What point is on the graph of $f$ ? (c) If $f(x)=-1$ , what is $x$ ? What point(s) is/are on the graph of $f$ ? (d) What is the domain of $f$ ? (e) List the x-intercept(s), if any, of the graph of f . (f) List the $y$ -intercept, if there is one, of the graph of f .

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Problem 588

Answer the questions about the following function. $f(x)=4 x^{2}-x-3$ (a) Is the point $(2,11)$ on the graph of $f$ ? (b) If $x=-2$ , what is $f(x)$ ? What point is on the graph of $f$ ? (c) If $f(x)=-3$ , what is $x$ ? What point(s) is/are on the graph of $f$ ? (d) What is the domain of $f$ ? (e) List the $x$ -intercept(s), if any, of the graph of $f$ . (f) List the $y$ -intercept, if there is one, of the graph of f .

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Problem 589

Question Watch Videc
Solve for the roots in simplest form using the quadratic formula: $4 x^{2}+37=-20 x$
Answer Attempt 2 out of 2

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Problem 590

ation in standard form. $h(x)=-2(x+1)^{2}+9$

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Problem 591

3.
If Josselyn solved a quadratic equation by factoring and her solutions were $x=-5$ and $x=\frac{4}{3}$ , which of the following is equivalent to Josselyn's quadratic equation?

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Problem 592

- Question 9 of 12 (1 point) I Question Attempt: 1 of 1
Graph the parabola. $y=-3 x^{2}-24 x-45$

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Problem 593

Solve the equation. (Enter your answers as a comma-separated list.) $\begin{array}{l} z^{2}+12 z+35=0 \\ z=1 \end{array}$

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Problem 594

What is the discriminant of $9 x^{2}+2=10 x ?$ $-356$ $-172$ 28 72

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Problem 595

Question 1 of 9, Step 1 of 1 $0 / 12$ Correct
Identify the correct graph and the $x$ -and $y$ -intercepts of the following polynomial function. Express all points as ordered pairs. $r(x)=x^{2}-x-6$
Answer

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Problem 596

$y=(x-2)^{2}+2$
What transformations have occurred?
Right 2 and down 2 Right 2 and up 2 Left 2 and up 2 Left 2 and down 2 Scarleth 5

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Problem 597

G. $y=(x)^{2}+7$ B. $y=(x+7)^{2}$ c. $y=(x)^{2}-7$ D. $y=(x-7)^{2}$
Match the description to its equation. Moves right 7
B C A D Scarleth $s$

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Problem 598

$y=-(x)^{2}-4$
Match the equation to its description.
Reflected over $x$ axis and left 4
Reflected over $x$ axis and right 4
Reflected over $x$ axis and up 4
Reflected over $x$ axis and down 4 Scarleth S

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Problem 599

Using the quadratic formula to solve $x^{2}+20=2 x$ , what are the values of $x ?$ $1 \pm \sqrt{21}$ $-1 \pm \sqrt{19} i$ $1 \pm 2 \sqrt{19}$ i $1 \pm \sqrt{19} i$

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Problem 600

11/16
Which transformation maps the graph of $f(x)=x^{2}$ to the graph of $g(x)=(x+4)^{2}$ ?
4 units to the left 4 units to the right 4 units up a reflection across the $x$ axis

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Quadratics

Problem 501

Identify the vertex and the axis of symmetry for the function. g(x)=(x−44)2g(x)=(x-44)^{2}g(x)=(x−44)2The vertex of the function is □\square□ (Type an ordered pair.)

Problem 502

Solve for yyy. (y−2)2=2y2−12y+16(y-2)^{2}=2 y^{2}-12 y+16(y−2)2=2y2−12y+16If there is more than one solution, separate them with commas.

Problem 503

Rewrite without parentheses and simplify. (5y+6v)2(5 y+6 v)^{2}(5y+6v)2

Problem 504

i) Faktorkan selengkapnya Factorise completely 6m2−7m−206 m^{2}-7 m-206m2−7m−20Jawapan / Answer.

Problem 505

(x+5)2−16=0(x+5)^{2}-16=0(x+5)2−16=0

Problem 506

Question Watch VideoSolve for all values of xxx by factoring. x2−4x−59=−4x+5x^{2}-4 x-59=-4 x+5x2−4x−59=−4x+5Answer Attempt 1 out of 2

Problem 507

Watch VideoSolve for all values of xxx by factoring. x2+10x−40=4xx^{2}+10 x-40=4 xx2+10x−40=4x

Problem 508

Solve the quadratic by factoring. 3x2+12x=7x+23 x^{2}+12 x=7 x+23x2+12x=7x+2

Problem 509

Problem 510

Question Watch vvvSolve the quadratic by factoring. 5x2−20x+14=2x+65 x^{2}-20 x+14=2 x+65x2−20x+14=2x+6

Problem 511

Question Watch VideoFactor completely. 4x2−64x+2524 x^{2}-64 x+2524x2−64x+252Answer Attempt 1 out of 2

Problem 512

What are the solutions to 2x2+8x+4=02 x^{2}+8 x+4=02x2+8x+4=0 ? x=−6±2x=-6 \pm \sqrt{2}x=−6±2​ x=−6±62x=-6 \pm 6 \sqrt{2}x=−6±62​ x=−2±2x=-2 \pm \sqrt{2}x=−2±2​ x=−2±303x=-2 \pm \frac{\sqrt{30}}{3}x=−2±330​​

Problem 513

Problem 514

Graph f(x)=−12x2−x−32f(x)=-\frac{1}{2} x^{2}-x-\frac{3}{2}f(x)=−21​x2−x−23​ using the Quadratic Formula. State both coordinates of the xxx-intercept, yyy-intercept, and vertex.

Problem 515

f(x)=5x2+30x+42f(x)=5 x^{2}+30 x+42f(x)=5x2+30x+42In vertex form f(x)=a(x−h)2+kf(x)=a(x-h)^{2}+kf(x)=a(x−h)2+k the value of a=a=a= □\square□ the value of h=h=h= □\square□ and the value of k=k=k= □\square□

Problem 516

Problem 517

Select the quadratic equation in vertex form AND standard form. (11x+4)2(11 x+4)^{2}(11x+4)2 x2+811x+16121x^{2}+\frac{8}{11} x+\frac{16}{121}x2+118​x+12116​

Problem 518

Problem 519

Problem 520

Solve for www. w2−9w+14=0w^{2}-9 w+14=0w2−9w+14=0If there is more than one solution, separate them wit If there is no solution, click on "No solution."

Problem 521

Question Watch Video Show ExamplesWrite two numbers that multiply to the value on top and add to the value on bottom.

Problem 522

Question Watch Video Show ExamplesWrite two numbers that multiply to the value on top and add to the value on bottom.

Problem 523

Problem 524

Problem 525

Solve by using the quadratic formula: 6x2+3x−7=06 x^{2}+3 x-7=06x2+3x−7=0.

Problem 526

3=x2+2x3=x^{2}+2 x3=x2+2x

Problem 527

Problem 528

0. Determine and interpret the zeros in terms of the context. A company's profit in the years since 2000 is modeled by the equation: C(x)=−2x2+20x+48C(x)=-2 x^{2}+20 x+48C(x)=−2x2+20x+48.

Problem 529

Problem 530

2. Which of the following represents the yyy-intercept of the graph of the quadratic function y=2x2−7x+9y=2 x^{2}-7 x+9y=2x2−7x+9 ? (Recall, that the yyy-intercept of a graph always occurs when x=0x=0x=0.) (1) 7 (3) -7 (2) 2 (4) 9

Problem 531

Problem 532

Use the following information to answer the question.If the equation for the above function is written in the form y=ax2+bx+cy=a x^{2}+b x+cy=ax2+bx+c, the value of aaa isSelect one: a. either positive or negative b. negative c. positive d. dependent on the value of ccc

Problem 533

Graph the functions on the same coordinate plane. f(x)=−2xg(x)=x2−3\begin{array}{l} f(x)=-2 x \\ g(x)=x^{2}-3 \end{array}f(x)=−2xg(x)=x2−3​What are the solutions to the equation f(x)=g(x)f(x)=g(x)f(x)=g(x) ? Select each correct answer. There are two.Select 2 correct answer(s)1 -3 -2 0

Problem 534

Solve for a. 5a2=9805 a^{2}=9805a2=980Select both solutions.Select 2 correct answer(s) -196 -14 196 14

Problem 535

x2+4y2−6x+16y+21=0x^{2}+4 y^{2}-6 x+16 y+21=0x2+4y2−6x+16y+21=0

Problem 536

Problem 537

6+ y = (x+ (x + 1)(x-5) 2 4+ -3-2 -1 0 2 3 4 5

Problem 538

Factor the equation completely. y2+3y−28y^{2}+3 y-28y2+3y−28Factored Form □\square□

Problem 539

2. A rectangle has dimensions x+10x+10x+10 2x−32 \mathrm{x}-32x−3, where x is in centimetres. Tir area of the rectangle is 54 cm254 \mathrm{~cm}^{2}54 cm2. b) What is the value of xxx ? 2x2−17x−84=02 x^{2}-17 x-84=02x2−17x−84=0

Problem 540

Problem 541

Problem 542

3. Which equation has imaginary roots? (1) x2−1=0x^{2}-1=0x2−1=0 (2) x2−2=0x^{2}-2=0x2−2=0 (3) x2+x+1=0x^{2}+x+1=0x2+x+1=0 (4) x2−x−1=0x^{2}-x-1=0x2−x−1=0

Problem 543

Problem 544

Problem 545

Problem 546

Describe the transformation from the parent function. (Mark all that apply) y=−(x+3)2+2y=-(x+3)^{2}+2y=−(x+3)2+2 Reflected across the yyy-axis Shifted up 2 units Shifted right 3 units Vertex is (−3,2)(-3,2)(−3,2) Shifted left 3 units Shifted up 3 units Reflected across the x-aris

Problem 547

Sketch the graph of each inequality. 4) y≤−x2+8x−12y \leq-x^{2}+8 x-12y≤−x2+8x−12 A) C) B) D)

Problem 548

Identify the vertex and the axis of symmetry for the function. $g(x)=(x-44)^{2}$
The vertex of the function is $\square$ (Type an ordered pair.)

Solve for $y$ . $(y-2)^{2}=2 y^{2}-12 y+16$
If there is more than one solution, separate them with commas.

Rewrite without parentheses and simplify. $(5 y+6 v)^{2}$

i) Faktorkan selengkapnya Factorise completely $6 m^{2}-7 m-20$
Jawapan / Answer.

$(x+5)^{2}-16=0$

Question Watch Video
Solve for all values of $x$ by factoring. $x^{2}-4 x-59=-4 x+5$
Answer Attempt 1 out of 2

Watch Video
Solve for all values of $x$ by factoring. $x^{2}+10 x-40=4 x$

Solve the quadratic by factoring. $3 x^{2}+12 x=7 x+2$

Question Watch $v$
Solve the quadratic by factoring. $5 x^{2}-20 x+14=2 x+6$

Question Watch Video
Factor completely. $4 x^{2}-64 x+252$
Answer Attempt 1 out of 2

What are the solutions to $2 x^{2}+8 x+4=0$ ? $x=-6 \pm \sqrt{2}$ $x=-6 \pm 6 \sqrt{2}$ $x=-2 \pm \sqrt{2}$ $x=-2 \pm \frac{\sqrt{30}}{3}$

Graph $f(x)=-\frac{1}{2} x^{2}-x-\frac{3}{2}$ using the Quadratic Formula. State both coordinates of the $x$ -intercept, $y$ -intercept, and vertex.

$f(x)=5 x^{2}+30 x+42$
In vertex form $f(x)=a(x-h)^{2}+k$ the value of $a=$ $\square$ the value of $h=$ $\square$ and the value of $k=$ $\square$

Select the quadratic equation in vertex form AND standard form. $(11 x+4)^{2}$ $x^{2}+\frac{8}{11} x+\frac{16}{121}$

Solve for $w$ . $w^{2}-9 w+14=0$
If there is more than one solution, separate them wit If there is no solution, click on "No solution."

Question Watch Video Show Examples
Write two numbers that multiply to the value on top and add to the value on bottom.

Question Watch Video Show Examples
Write two numbers that multiply to the value on top and add to the value on bottom.

Solve by using the quadratic formula: $6 x^{2}+3 x-7=0$ .

$3=x^{2}+2 x$

0. Determine and interpret the zeros in terms of the context. A company's profit in the years since 2000 is modeled by the equation: $C(x)=-2 x^{2}+20 x+48$ .

2. Which of the following represents the $y$ -intercept of the graph of the quadratic function $y=2 x^{2}-7 x+9$ ? (Recall, that the $y$ -intercept of a graph always occurs when $x=0$ .) (1) 7 (3) -7 (2) 2 (4) 9

Use the following information to answer the question.
If the equation for the above function is written in the form $y=a x^{2}+b x+c$ , the value of $a$ is
Select one: a. either positive or negative b. negative c. positive d. dependent on the value of $c$

Graph the functions on the same coordinate plane. $\begin{array}{l} f(x)=-2 x \\ g(x)=x^{2}-3 \end{array}$
What are the solutions to the equation $f(x)=g(x)$ ? Select each correct answer. There are two.
Select 2 correct answer(s)
1 -3 -2 0

Solve for a. $5 a^{2}=980$
Select both solutions.
Select 2 correct answer(s) -196 -14 196 14

$x^{2}+4 y^{2}-6 x+16 y+21=0$

Factor the equation completely. $y^{2}+3 y-28$
Factored Form $\square$

2. A rectangle has dimensions $x+10$ $2 \mathrm{x}-3$ , where x is in centimetres. Tir area of the rectangle is $54 \mathrm{~cm}^{2}$ . b) What is the value of $x$ ? $2 x^{2}-17 x-84=0$

3. Which equation has imaginary roots? (1) $x^{2}-1=0$ (2) $x^{2}-2=0$ (3) $x^{2}+x+1=0$ (4) $x^{2}-x-1=0$

Describe the transformation from the parent function. (Mark all that apply) $y=-(x+3)^{2}+2$ Reflected across the $y$ -axis Shifted up 2 units Shifted right 3 units Vertex is $(-3,2)$ Shifted left 3 units Shifted up 3 units Reflected across the x-aris

Sketch the graph of each inequality. 4) $y \leq-x^{2}+8 x-12$ A) C) B) D)

789074 $: 3$ 90
Determine the domain and range of the quadratic function shown on the graph. Select two answers.
Select all correct options
$\mathrm{D}: \mathrm{x} \leq-1$ $R: y \leq-1$ D: all real numbers R: all real numbers

How many solutions can a quadratic have?
1,2, or 3 none, 1, or 2 none or 2 1 or 2

Find all $y$ -intercepts and $x$ -intercepts of the graph of the function. $f(x)=2 x^{2}-15 x+18$
If there is more than one answer, separate them with commas. Click on "None" if applicable.

$12 x^{2}+10 x-6=-26 x+15$

\%kuta Software - Infinite Algebra 1 Factoring Trinomials $(a>1)$ Factor each completely. 1) $3 p^{2}-2 p-5$

Name: $\qquad$ D.
10. Factor this polynomial: $6 x^{2}-13 x-28$
A $(2 x+7)(3 x+4)$ C $(2 x+7)(3 x-4)$
18. $(2 x-7)(3 x-4)$ (D) $(2 x-7)(3 x+4)$

Complete the square for $h(x)=5 x^{2}+20 x-60$ $\begin{array}{l} x=-2 \\ h(x)=5 x^{2}+2 \\ h(-2)=-80 \\ (-2,-80) \end{array}$

Solve for x . $\begin{array}{c} 4 x^{2}+4 x+1=0 \\ x=-\frac{[?]}{} \end{array}$

The graph of a function $g$ is shown below. Find $g(-2)$ and find one value of $x$ for which $g(x)=-5$ . (a) $g(-2)=$ $\square$ (b) One value of $x$ for which $g(x)=-5: 0$

Which type of conic is represented by the equation below? $x=-3 y^{2}+30 y-80$
This is an equation of a parabola. Write the equation of this conic section in conic form.

Graph the function. $1 / 5$ $h(x)=-\frac{1}{2} x^{2}$
Plot five points on the graph of the function: one point with $x=0$ , two points with negative $x$ -values, and two points with positive $x$ -values. Then click on the graph-a-function button.

Factor fully, if possible. a) $x^{2}+7 x+12$

Question Whatan Vifies
Write two numbers that multiply to the value on top and add to the value ne bretloe

$y=-2 x^{2}+24 x+5$
Convert to vertex form. $y=-2(x-6)^{2}+77 \quad y=-2(x+6)^{2}+77$ $y=-2(x-12)^{2}+77$ $y=-2(x+12)^{2}+77$ Makenzie Armstrong

Graph the function using its vertex, axis of symmetry, and intercepts. $f(x)=-x^{2}+6 x-8$

Convert $f(x)=3 x^{2}+6 x-5$ to vertex form. $f(x)=3(x+2)^{2}-8$ $f(x)=3(x-1)^{2}-8$ $f(x)=3(x-2)^{2}-8$ $f(x)=3(x+1)^{2}-8$ Makenzie Armstrong

$\begin{array}{l} g(x)=x^{2}+6 x \\ h(x)=x^{2}-1 \end{array}$
Write $g(h(x))$ as an expression in terms of $x$ . $g(h(x))=\square \quad 7$

What are the solutions to (2 Points) $2 x^{2}+x-3$ 1 $3,-\frac{1}{2}$ $-1, \frac{3}{2}$ $1,-\frac{3}{2}$

5 Numeric 1 point
Enter a decimal approximation of the rightmost x-intercept of $f(x)=x^{2}+4 x-1$ . Must be after the decimal point.)

-31 $-9$ $\frac{1}{31}$ $\frac{1}{9}$