Quadratics

Problem 2501

Solve for $x$ using the quadratic formula: $4 x^{2} = -8 x + 1$ . Round to the nearest hundredth.

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Problem 2502

Solve $2 x^{2}-2 x-7=0$ using the quadratic formula. Round to the nearest hundredth. Provide all solutions.

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Problem 2503

A ball starts at 3 m height with a 5 m/s upward speed. Find $t$ when height $h=4$ m using $h=3+5t-5t^2$ . Round to nearest hundredth.

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Problem 2504

A ball starts at 3 m high with a speed of $5 \mathrm{~m/s}$ . Its height after $t$ seconds is $h=3+5t-5t^2$ . Find $t$ when $h=4$ m. Round to the nearest hundredth.

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Problem 2505

Find $t$ when the rocket's height $h=82$ ft, given $h=202t-16t^2$ . Round to the nearest hundredth.

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Problem 2506

A ball is thrown from 25 m with an initial downward velocity of $5 \mathrm{~m} / \mathrm{s}$ . When does it hit the ground? Use $h=25-5t-5t^{2}$ . Round to the nearest hundredth.

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Problem 2507

Find all values of $t$ where the rocket's height $h=39$ feet, given $h=113t-16t^2$ . Round to the nearest hundredth.

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Problem 2508

A ball is thrown from 1 m high with an initial velocity of $13 \mathrm{~m/s}$ . Find $t$ when $h=8$ m: $h=1+13t-5t^2$ . Round to nearest hundredth.

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Problem 2509

A ball starts at 7 ft high and is thrown up at 36 ft/s. Find $t$ when the height $h=19$ ft using $h=7+36t-16t^2$ . Round to nearest hundredth.

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Problem 2510

Solve the equation $x^{2}-x-20=0$ .

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Problem 2511

A delivery person drives $f(x)=x^{2}+3x$ miles in $x$ hours. For $y$ miles, gas used is $g(y)=\frac{y}{18}$ . In 9 hours, how many gallons needed?

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Problem 2512

Save \& Exit Certify Lesson: Chapter 7 Review
Question 14 of 18, Step 1 of 1 21/27 Correc
Solve the following quadratic equation using the quadratic formula. $-x^{2}=8$
Answer

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Problem 2513

Using algebraic methods, find the solution sets for the following. Give your solutions in interval notation. (a) $6 x^{2} \geq 24 x-18$ (b) $\frac{3}{x+1}<15$

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Problem 2514

Question 10 10 pts
The complex roots of the graph above are $x \pm y i$ .
What is the value of $x$ ? $\square$ 2 $\square$ What is the value of $y$ ?

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Problem 2515

What is the axis of symmetry of the parabola $y=5 x^{2}+3 ?$ $\square$
Save answer

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Problem 2516

Question Determine the domain and range of the following parabola. $f(x)=2(x-2)^{2}+1$
Select the correct answer below: Domain is all real numbers. Range is $f(x) \leq 2$ Domain is all real numbers. Range is $f(x) \geq 1$ Domain is all real numbers. Range is $f(x) \geq 2$ Domain is all real numbers. Range is $f(x) \leq 1$

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Problem 2517

Question Find the $y$ -intercept of the following function. $f(x)=12 x^{2}-4 x-21$
Give your answer as an ordered pair.

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Problem 2518

Question Find the $x$ -intercept(s) of the following function. $f(x)=12 x^{2}-4 x-21$
Select all correct answers.

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Problem 2519

Question Watch $V$
Solve the following quadratic equation for all values of $x$ in simplest form. $(x-6)^{2}-23=-12$
Answer Attempt 1 out of 2

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Problem 2520

Question Watch Video Show Examples
If using the method of completing the square to solve the quadratic equation $x^{2}+8 x+37=0$ , which number would have to be added to "complete the square"? Answer Attempt 1 out of 2

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Problem 2521

على يغة مستطيل الشكل يزيد طولها عرضها به قدار 4000, ومساحتها 48000m / يريد مزارها أماطتها بسياج أجد طول السياج 2

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Problem 2522

Solve for $k$ . $36 k^{2}-13 k+1=0$
Write each solution as an integer, proper fraction, or improper fraction in simplest form. If there are multiple solutions, separate them with commas. $k=$ $\square$

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Problem 2523

Find the $x$ -intercepts of the parabola with vertex $(6,27)$ and $y$ -intercept $(0,-81)$ . Round to the nearest hundredth.

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Problem 2524

Find the value of $y$ for the equation $y=-5 x^{2}-10 x-15$ .

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Problem 2525

The product of two consecutive, nonnegative integers is 342 . Find the integers and separate them with a comma.

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Problem 2526

Backspace
A stone fall from a railroad overpass which is 36 ft high into the path of a train which is approaching the overpass with uniporm speced It the stone falls when the train is 50 ft away from the overpass and thestome hit the gmind just as the train anives at that spot, how fast is the train movin

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Problem 2527

Graph the function. Label the $x$ -intercept(s), vertex, and axis of symmetry.
21. $f(x)=(x-3)(x+1)$
22. $h(x)=x(x+6)$

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Problem 2528

Factor each quadratic expression. (10) $x^{2}+5 x+6$ (12) $x^{2}-5 x+4$ $13 x^{2}-4 x-12$

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Problem 2529

Solve the equation by factoring. Check your solution. If there are multiple solutions, list the solutions from least to greatest separated by a comma. Leave in simplest fractional form. $2 x^{2}-x-3=0$ $\square$

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Problem 2530

Find the $x$ -intercepts of the parabola with vertex $(1,245)$ and $y$ -intercept $(0,240)$ . Round to the nearest hundredth.

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Problem 2531

Solve the inequality $2x - 8 \geq -3x^2$ and express the solution in interval notation.

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Problem 2532

Find $x$ such that $f(x)=0$ for $f(x)=x^{2}-6x+9$ . Options: A) -3 B) 0 C) 3 D) 9

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Problem 2533

Find the equivalent expression for $2 x^{2}-14 x+24$ from the options: A, B, C, D.

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Problem 2534

Find the solutions to $2 x^{2} = -10 x + 12$ . Select from: $x=1, x=6, x=-3, x=-6, x=-2, x=3$ .

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Problem 2535

Find the solutions for $2 x^{2} = -10 x + 12$ . Choose from: $x=1$ , $x=6$ , $x=-3$ , $x=-6$ , $x=-2$ , $x=3$ .

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Problem 2536

Find the $y$ -intercept of the quadratic function $f(x)=a(x-p)(x-q)$ using $a$ , $p$ , and $q$ .

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Problem 2537

Find the function $g$ from the transformations of $f(x)=x^{2}$ : vertical stretch by 2, reflection, then translate. Which is $g$ ? a. $g(x)=-2(x+1)^{2}-4$ b. $g(x)=-2(x+1)^{2}+8$ c. $g(x)=2(-x+1)^{2}-4$ d. $g(x)=-2(x-1)^{2}-4$

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Problem 2538

कौन-सा द्विघात समीकरण नहीं है: (a) $(x-5)(3 x+2)=x(x+3)$ , (b) $(2 x-2)(x+3)=(x+5)(2 x+5)$ , (c) $(x+3)^{2}=\left(3 x^{2}+2 x+1\right)$ , (d) $x^{3}+x^{2}+x+1=(x+1)^{3}$ ?

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Problem 2539

Solve the equation $e^{2}+6 e+8=0$ .

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Problem 2540

Solve the equation $g^{2}+8g+7=0$ .

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Problem 2541

Solve the quadratic equation: $k^{2}+10k+16=0$ .

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Problem 2542

Solve the equation by factoring. Check your solution. If there are multiple solutions, list the solutions from leas greatest separated by a comma. $x^{2}+4=0$ $\square$

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Problem 2543

4) Through: $(2,-1)$ Vertex: $(3,6)$

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Problem 2544

For the parabola $y=-2 x^{2}+4 x-3$ find the vertex. $(4,-3)$ $(1,-1)$ $(-1,1)$ $(-3,4)$

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Problem 2545

Find the discriminant of the equation $5 x^{2}+7 x+3=0$ . 28 34 $-11$ $-53$

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Problem 2546

Exponents and Polymomials Factoring a quadratic with leading coefficient greater than 1
Factor. $5 z^{2}-18 z-8$

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Problem 2547

Q Exponents and Polynomials Factoring a quadratic with leading coefficient greater than 1
Factor. $8 x^{2}+18 x+9$ $\square$

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Problem 2548

This quiz: 10 point(s) possible This question: 1 point(s) possible
Suppose that the manufacturer of a gas clothes dryer has found that when the unit price is p dollars, the revenue $R$ (in dollars) is $R(p)=-2 p^{2}+2,000 p$ . (a) At what prices $p$ is revenue zero? (b) For what range of prices will revenue exceed $\$ 400,000$ ? (a) At what prices $p$ is revenue zero?
The revenue equals zero when $p$ is $\$$ $\square$ (Use a comma to separate answers, but do not use commas in any individual numbers.) (b) For what range of prices will revenue exceed $\$ 400,000$ ? $\square$ (Type your answer i

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Problem 2549

侪 $\sqrt{2}$ Write the equation in standard form for the hyperbola $-2 x^{2}+y^{2}+12 y-32=0$ $\square$ 믐 () 2 Submit

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Problem 2550

15. What are the solutions for the quadratic function $y=3 x^{2}-8 x+7$ ? $x=\frac{4 \pm i \sqrt{5}}{3}$ $x=\frac{-4 \pm i \sqrt{5}}{3}$ $x=-6 ; x=14$ $x=\frac{8 \pm \sqrt{20}}{6}$

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Problem 2551

Quadratic Formula
Solve for x . $\begin{array}{c} x^{2}-5 x-24=0 \\ x=[?] \end{array}$
Remember the quadratic formula: $x=\frac{-b \pm \sqrt{b^{2}-4 a c}}{2 a}$

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Problem 2552

atic by factoring. $2 x^{2}+9 x-1=2 x-7$

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Problem 2553

New! Multi Part Question - when you answer this question we'll mark each part individually Bookwork code: 1E Calculator allowed
Work out the solutions to these simultaneous equations: $\begin{aligned} x & =5-y \\ y^{2} & =3 x+28 \end{aligned}$
If any of your answers are decimals, give them to 2 d.p.

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Problem 2554

If the range of a quadratic function is $5 \leq y<\infty$ , which of the following could be true? None of these are correct. The parabola has a maximum at $(2,5)$ . The parabola has a minimum at $(2,1)$ . The parabola has a maximum at $(5,1)$ .

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Problem 2555

a) Factorise $x^{2}+9 x+14$ . b) By sketching a graph, solve the inequality $x^{2}+9 x+14 \leq 0$ .

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Problem 2556

A bridge is supported by three arches. The function that describes the arches is $h(x)=-0.25 x^{2}+2.375 x$ , where $h(x)$ is the height, in metres, of the arch above the ground at any distance, $x$ , in metres, from one end of the bridge. How far apart ar the bases of each arch? 1) 9.5 m 2) 9.2 m 3) 8.6 m 4) 10.3 m

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Problem 2557

How many zeros does $f(x)=a(x-5)^{2}$ have if $a<0$ ? 1) It is impossible to determine. 2) 1 3) 0 4) 2

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Problem 2558

uestion 34 (2 points) A quadratic function has an equation that can be written in the form $f(x)=a(x-H(x-$ s). The graph of the function has $x$ -intercepts at $(-4,0)$ and $(2,0)$ and passes through the point $(-2,-8)$ . Write the equation of the function.

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Problem 2559

What are the solutions to $100 x^{2}-1=0$ ? Use the keypad to enter your answers in the boxes. Find more symbols by using the drop-down arrow at the top of the keypad.
The solutions to the quadratic equation are $x=$ $\square$ and $x=$ $\square$

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Problem 2560

Solve using the quadratic formula. $k^{2}-k-4=0$
Write your answers as integers, proper or improper fractions in simplest form, or decimals rounded to the nearest hundredth. $k=$ $\square$ or $k=$ $\square$ Submit

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Problem 2561

Solve using the quadratic formula. $-2 t^{2}+9 t+7=0$
Write your answers as integers, proper or improper fractions in simplest form, or decimals rounded to the nearest hundredth. $t=$ $\square$ or $t=$ $\square$

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Problem 2562

6. Untersuchung von Funktionenscharen
Untersuchen Sie die Schar $f_{a}$ auf Nullstellen und Extrema. Zeichnen Sie $f_{a}$ . Es gelte $a>0$ . a) $f_{a}(x)=-\frac{1}{a} x^{2}+a x$ ,

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Problem 2563

CCA2 > Chapter 2 > Lesson 2.1.2 > Problem 2-24
Consider the equations $y=3(x-1)^{2}-5$ and $y=3 x^{2}-6 x-2$ . a. Verify that they are equivalent by creating a table or graph for each equation. $\square$ $\checkmark$ Hint (a): Here are a couple of points on the table. Make sure you get these points and continue both of your tables for at leas \begin{tabular}{c|c|} \hline $x$ & $y$ \\ \hline-2 & 22 \\ \hline-1 & \\ \hline 0 & \\ \hline 1 & -5 \\ \hline 2 & \\ \hline \end{tabular}

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Problem 2564

Solve for $y$ . $y^{2}-6 y+8=0$

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Problem 2565

Rewrite $x^{2}+14 x-10=0$ in the form $(x-p)^{2}=q$ by completing the square. Use the keypad to enter your answer in the box. Find more symbols by using the drop-down arrow at the top of the keypad. $x^{2}+14 x-10=0$ in the form $(x-p)^{2}=q$ is $\square$ 7.

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Problem 2566

34) Henry throws a tennis ball over his house. The ball is 6 feet above the ground when he lets it go. The quadratic function that models the height, in feet, of the ball after $t$ seconds is $y=-16 t^{2}+46 t+6$ . a. How long does it take for the ball to hit the ground? Roughly sketch the graph. b. There is a trampoline on the other side that is 5 feet off the ground. The ball happens to land on it instead of the ground. How long would this take? Create a new equation and solve.

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Problem 2567

Algebra 1 Y. 4 Transformations of quadratic functions 6 YS
Find $g(x)$ , where $g(x)$ is the translation 1 unit left of $f(x)=x^{2}$ . Video Questions answered
Write your answer in the form $a(x-h)^{2}+k$ , where $a$ , $h$ , and $k$ are integers. $g(x)=$ $\square$ ( $\square$ ) 2 Time elapsed 00 01 07 1 HR MIN sec SmartScore Submit out of 100 15

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Problem 2568

(2 points) Find all solutions to the system of nonlinear equations. $\begin{array}{c} y=x-7 \\ x^{2}+y^{2}=37 \end{array}$
Solution(s): $\square$ help (points)
Enter the solution as an ordered pair, $(a, b)$ or a list of ordered pairs, $(a, b),(c, d)$ .

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Problem 2569

Solve the equation $(x-1)(x-3)=0$ for the values of $x$ .

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Problem 2570

Solve the equation: $(x-1)(x-3)=0$

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Problem 2571

Solve the equation $x^{2}-32=0$ to find $x$ algebraically and graphically.

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Problem 2572

Graph the function $f(x)=-x^{2}+4x+1$ and find its vertex, max/min, axis of symmetry, intercepts, domain, and range.

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Problem 2573

Solve the inequality: $9x - 9 \geq -4x^2$ . Provide the solution in interval notation.

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Problem 2574

Rewrite $f(x)=x^{2}+6 x$ in vertex form and find its roots (i.e. $x$ -intercepts).

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Problem 2575

Find the composite functions for $f(x)=8x+4$ and $g(x)=x^{2}$ : (a) $f \circ g$ , (b) $g \circ f$ , (c) $f \circ f$ , (d) $g \circ g$ . Also, state the domain for each function.

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Problem 2576

A rectangle's length is $5 \mathrm{ft}$ more than twice the width, with an area of $42 \mathrm{ft}^{2}$ . Find its dimensions.

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Problem 2577

Find Revenue, Cost, and Profit for selling $x$ thousand items with price \ $3.00, fixed cost \$143,185, and variable cost$ -3x^{2}+3480x-100$.

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Problem 2578

A rocket is launched from a tower. The height of the rocket, y in feet, is related to the time after launch, x in seconds, by the given equation. Using this equation, find the maximum height reached by the rocket, to the nearest tenth of a foot. $y=-x^{2}+6 x$

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Problem 2579

Determine whether the equation is quadratic. $3 x+2=0$

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Problem 2580

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. $g(x)=$

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Problem 2581

10/10
A quadratic is reflected down when the value of $a$ is negative.
TRUE FALSE

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Problem 2582

Which value must be added to the expression $x^{2}+12 x$ to make it a perfect-square trinomial? 6 36 72 144

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Problem 2583

Solve for $x$ in the equation $x^{2}+2 x+1=17$ $x=-1 \pm \sqrt{15}$ $x=-1 \pm \sqrt{17}$ $x=-2 \pm 2 \sqrt{5}$ $x=-1 \pm \sqrt{13}$

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Problem 2584

Solve for $x$ in the equation $2 x^{2}+3 x-7=x^{2}+5 x+39$ $x=-6 \pm \sqrt{82}$ $x=-6 \pm 2 \sqrt{17}$ $x=1 \pm \sqrt{33}$ $x=1 \pm \sqrt{47}$

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Problem 2585

Solve for $x$ in the equation $x^{2}+14 x+17=-96$ - $x=-7 \pm 4 \sqrt{6} i$ $x=-7 \pm 8 i$ $x=7 \pm 4 \sqrt{6} ;$ $x=7 \pm 8 i$

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Problem 2586

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

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Problem 2587

Practice:
1. Noah solved the equation $5 x^{2}=45$ . Here are the steps: $\begin{array}{c} 5 x^{2}=45 \\ x^{2}=9 \\ x=3 \end{array}$
Do you agree with Noah? Explain your reasoning.

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Problem 2588

13. Let $x$ represent the number of bags of gummy snails produced and sold in a typical week. At Blerta's Candy Marketplace, the demand function for bags of gummy snails (price in dollars per bag) is given by $p(x)=-.09 x+8$ and the cost (in dollars) of producing $x$ bags of gummy snails is given by $C(x)=0.35 x+12$ a. (4 points) Find and interpret $C(0)$ b. (2 points) Find the number of bags of gummy snails produced and sold in a typical week when the price per bag is $\$ 3.50$ . c. (4 points) Suppose the weekly profit function was found to be $P(x)=-.09 x^{2}+7.65 x-12$ . Find the vertex of $y=P(x)$ . Then find the maximum profit.

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Problem 2589

TEST CONTINUED Complete the square and write the equation in standard form. Then give the center and radius of the circle. 9) $x^{2}+6 x+9+y^{2}-2 y+1=64$

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Problem 2590

What is the axis of symmetry of the parabola $y=5(x-6)^{2}-7 ?$

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Problem 2591

Solve using the quadratic formula. $-3 w^{2}+8 w-2=0$

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Problem 2592

Solve. Select all that apply. $x^{2}+5 x-36<0$

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Problem 2593

7. Luke Strong, the human cannonball, flies through the air on a path that can be modeled by $h(d)=-3.9 d^{2}+13.1 d+8.7$ where $d$ is the horizontal distance, in metres, from the launch point and $h$ is the height, in metres, above the ground. How far from the ramp does Luke land, to the nearest tenth of a metre? A. $\quad 0.6 \mathrm{~m}$ B. 2.0 m C. 3.9 m D. 7.9 m

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Problem 2594

PRACTISING
4. Determine the point(s) of intersection of each pair of functions. $\mathbf{K}_{\text {a) }} f(x)=-2 x^{2}-5 x+20, g(x)=6 x-1$ b) $f(x)=3 x^{2}-2, g(x)=x+7$ c) $f(x)=5 x^{2}+x-2, g(x)=-3 x-6$ d) $f(x)=-4 x^{2}-2 x+3, g(x)=5 x+4$

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Problem 2595

Bestimmen Sie die Nullstellen von $f(x)=2 x^{2}+4 x-16$ .

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Problem 2596

Identify a function $f(x)$ that passes through the points (0,0), (1,-2), and (2,0) from the options given.

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Problem 2597

Find a function $f(x)$ that passes through $(0,0),(1,-2),(2,0)$ from these options: $f(x)=2 x^{2}-4 x$ , $f(x)=-2 x^{2}$ , $f(x)=2 \sqrt{x}-4 x$ , $f(x)=-2 x$ .

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Problem 2598

Solve the equation using the quadratic formula: $4 n^{2} = -12 n - 7$ . Provide exact and approximate solutions.

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Problem 2599

Evaluate $2 x^{2}+2 x-16$ for $x=3$ .

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Problem 2600

Solve the equation $4n^{2} = -12n - 7$ using the quadratic formula. Provide exact and approximate solutions.

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1 ...23 24 25 26 27

Quadratics

Problem 2501

Solve for xxx using the quadratic formula: 4x2=−8x+14 x^{2} = -8 x + 14x2=−8x+1. Round to the nearest hundredth.

Problem 2502

Solve 2x2−2x−7=02 x^{2}-2 x-7=02x2−2x−7=0 using the quadratic formula. Round to the nearest hundredth. Provide all solutions.

Problem 2503

A ball starts at 3 m height with a 5 m/s upward speed. Find ttt when height h=4h=4h=4 m using h=3+5t−5t2h=3+5t-5t^2h=3+5t−5t2. Round to nearest hundredth.

Problem 2504

A ball starts at 3 m high with a speed of 5 m/s5 \mathrm{~m/s}5 m/s. Its height after ttt seconds is h=3+5t−5t2h=3+5t-5t^2h=3+5t−5t2. Find ttt when h=4h=4h=4 m. Round to the nearest hundredth.

Problem 2505

Find ttt when the rocket's height h=82h=82h=82 ft, given h=202t−16t2h=202t-16t^2h=202t−16t2. Round to the nearest hundredth.

Problem 2506

A ball is thrown from 25 m with an initial downward velocity of 5 m/s5 \mathrm{~m} / \mathrm{s}5 m/s. When does it hit the ground? Use h=25−5t−5t2h=25-5t-5t^{2}h=25−5t−5t2. Round to the nearest hundredth.

Problem 2507

Find all values of ttt where the rocket's height h=39h=39h=39 feet, given h=113t−16t2h=113t-16t^2h=113t−16t2. Round to the nearest hundredth.

Problem 2508

A ball is thrown from 1 m high with an initial velocity of 13 m/s13 \mathrm{~m/s}13 m/s. Find ttt when h=8h=8h=8 m: h=1+13t−5t2h=1+13t-5t^2h=1+13t−5t2. Round to nearest hundredth.

Problem 2509

A ball starts at 7 ft high and is thrown up at 36 ft/s. Find ttt when the height h=19h=19h=19 ft using h=7+36t−16t2h=7+36t-16t^2h=7+36t−16t2. Round to nearest hundredth.

Problem 2510

Solve the equation x2−x−20=0x^{2}-x-20=0x2−x−20=0.

Problem 2511

A delivery person drives f(x)=x2+3xf(x)=x^{2}+3xf(x)=x2+3x miles in xxx hours. For yyy miles, gas used is g(y)=y18g(y)=\frac{y}{18}g(y)=18y​. In 9 hours, how many gallons needed?

Problem 2512

Save \& Exit Certify Lesson: Chapter 7 ReviewQuestion 14 of 18, Step 1 of 1 21/27 CorrecSolve the following quadratic equation using the quadratic formula. −x2=8-x^{2}=8−x2=8Answer

Problem 2513

Using algebraic methods, find the solution sets for the following. Give your solutions in interval notation. (a) 6x2≥24x−186 x^{2} \geq 24 x-186x2≥24x−18 (b) 3x+1<15\frac{3}{x+1}<15x+13​<15

Problem 2514

Question 10 10 ptsThe complex roots of the graph above are x±yix \pm y ix±yi.What is the value of xxx ? □\square□ 2 □\square□ What is the value of yyy ?

Problem 2515

What is the axis of symmetry of the parabola y=5x2+3?y=5 x^{2}+3 ?y=5x2+3? □\square□Save answer

Problem 2516

Problem 2517

Question Find the yyy-intercept of the following function. f(x)=12x2−4x−21f(x)=12 x^{2}-4 x-21f(x)=12x2−4x−21Give your answer as an ordered pair.

Problem 2518

Question Find the xxx-intercept(s) of the following function. f(x)=12x2−4x−21f(x)=12 x^{2}-4 x-21f(x)=12x2−4x−21Select all correct answers.

Problem 2519

Question Watch VVVSolve the following quadratic equation for all values of xxx in simplest form. (x−6)2−23=−12(x-6)^{2}-23=-12(x−6)2−23=−12Answer Attempt 1 out of 2

Problem 2520

Question Watch Video Show ExamplesIf using the method of completing the square to solve the quadratic equation x2+8x+37=0x^{2}+8 x+37=0x2+8x+37=0, which number would have to be added to "complete the square"? Answer Attempt 1 out of 2

Problem 2521

على يغة مستطيل الشكل يزيد طولها عرضها به قدار 4000, ومساحتها 48000m / يريد مزارها أماطتها بسياج أجد طول السياج 2

Problem 2522

Solve for kkk. 36k2−13k+1=036 k^{2}-13 k+1=036k2−13k+1=0Write each solution as an integer, proper fraction, or improper fraction in simplest form. If there are multiple solutions, separate them with commas. k=k=k= □\square□

Problem 2523

Find the xxx-intercepts of the parabola with vertex (6,27)(6,27)(6,27) and yyy-intercept (0,−81)(0,-81)(0,−81). Round to the nearest hundredth.

Problem 2524

Find the value of yyy for the equation y=−5x2−10x−15y=-5 x^{2}-10 x-15y=−5x2−10x−15.

Problem 2525

The product of two consecutive, nonnegative integers is 342 . Find the integers and separate them with a comma.

Problem 2526

Problem 2527

Graph the function. Label the xxx-intercept(s), vertex, and axis of symmetry.21. f(x)=(x−3)(x+1)f(x)=(x-3)(x+1)f(x)=(x−3)(x+1)22. h(x)=x(x+6)h(x)=x(x+6)h(x)=x(x+6)

Problem 2528

Factor each quadratic expression. (10) x2+5x+6x^{2}+5 x+6x2+5x+6 (12) x2−5x+4x^{2}-5 x+4x2−5x+4 13x2−4x−1213 x^{2}-4 x-1213x2−4x−12

Problem 2529

Solve the equation by factoring. Check your solution. If there are multiple solutions, list the solutions from least to greatest separated by a comma. Leave in simplest fractional form. 2x2−x−3=02 x^{2}-x-3=02x2−x−3=0 □\square□

Problem 2530

Find the xxx-intercepts of the parabola with vertex (1,245)(1,245)(1,245) and yyy-intercept (0,240)(0,240)(0,240). Round to the nearest hundredth.

Problem 2531

Solve the inequality 2x−8≥−3x22x - 8 \geq -3x^22x−8≥−3x2 and express the solution in interval notation.

Problem 2532

Find xxx such that f(x)=0f(x)=0f(x)=0 for f(x)=x2−6x+9f(x)=x^{2}-6x+9f(x)=x2−6x+9. Options: A) -3 B) 0 C) 3 D) 9

Problem 2533

Find the equivalent expression for 2x2−14x+242 x^{2}-14 x+242x2−14x+24 from the options: A, B, C, D.

Problem 2534

Find the solutions to 2x2=−10x+122 x^{2} = -10 x + 122x2=−10x+12. Select from: x=1,x=6,x=−3,x=−6,x=−2,x=3x=1, x=6, x=-3, x=-6, x=-2, x=3x=1,x=6,x=−3,x=−6,x=−2,x=3.

Problem 2535

Find the solutions for 2x2=−10x+122 x^{2} = -10 x + 122x2=−10x+12. Choose from: x=1x=1x=1, x=6x=6x=6, x=−3x=-3x=−3, x=−6x=-6x=−6, x=−2x=-2x=−2, x=3x=3x=3.

Problem 2536

Find the yyy-intercept of the quadratic function f(x)=a(x−p)(x−q)f(x)=a(x-p)(x-q)f(x)=a(x−p)(x−q) using aaa, ppp, and qqq.

Problem 2537

Problem 2538

Problem 2539

Solve the equation e2+6e+8=0e^{2}+6 e+8=0e2+6e+8=0.

Problem 2540

Solve the equation g2+8g+7=0g^{2}+8g+7=0g2+8g+7=0.

Problem 2541

Solve the quadratic equation: k2+10k+16=0k^{2}+10k+16=0k2+10k+16=0.

Problem 2542

Solve for $x$ using the quadratic formula: $4 x^{2} = -8 x + 1$ . Round to the nearest hundredth.

Solve $2 x^{2}-2 x-7=0$ using the quadratic formula. Round to the nearest hundredth. Provide all solutions.

A ball starts at 3 m height with a 5 m/s upward speed. Find $t$ when height $h=4$ m using $h=3+5t-5t^2$ . Round to nearest hundredth.

A ball starts at 3 m high with a speed of $5 \mathrm{~m/s}$ . Its height after $t$ seconds is $h=3+5t-5t^2$ . Find $t$ when $h=4$ m. Round to the nearest hundredth.

Find $t$ when the rocket's height $h=82$ ft, given $h=202t-16t^2$ . Round to the nearest hundredth.

A ball is thrown from 25 m with an initial downward velocity of $5 \mathrm{~m} / \mathrm{s}$ . When does it hit the ground? Use $h=25-5t-5t^{2}$ . Round to the nearest hundredth.

Find all values of $t$ where the rocket's height $h=39$ feet, given $h=113t-16t^2$ . Round to the nearest hundredth.

A ball is thrown from 1 m high with an initial velocity of $13 \mathrm{~m/s}$ . Find $t$ when $h=8$ m: $h=1+13t-5t^2$ . Round to nearest hundredth.

A ball starts at 7 ft high and is thrown up at 36 ft/s. Find $t$ when the height $h=19$ ft using $h=7+36t-16t^2$ . Round to nearest hundredth.

Solve the equation $x^{2}-x-20=0$ .

A delivery person drives $f(x)=x^{2}+3x$ miles in $x$ hours. For $y$ miles, gas used is $g(y)=\frac{y}{18}$ . In 9 hours, how many gallons needed?

Save \& Exit Certify Lesson: Chapter 7 Review
Question 14 of 18, Step 1 of 1 21/27 Correc
Solve the following quadratic equation using the quadratic formula. $-x^{2}=8$
Answer

Using algebraic methods, find the solution sets for the following. Give your solutions in interval notation. (a) $6 x^{2} \geq 24 x-18$ (b) $\frac{3}{x+1}<15$

Question 10 10 pts
The complex roots of the graph above are $x \pm y i$ .
What is the value of $x$ ? $\square$ 2 $\square$ What is the value of $y$ ?

What is the axis of symmetry of the parabola $y=5 x^{2}+3 ?$ $\square$
Save answer

Question Find the $y$ -intercept of the following function. $f(x)=12 x^{2}-4 x-21$
Give your answer as an ordered pair.

Question Find the $x$ -intercept(s) of the following function. $f(x)=12 x^{2}-4 x-21$
Select all correct answers.

Question Watch $V$
Solve the following quadratic equation for all values of $x$ in simplest form. $(x-6)^{2}-23=-12$
Answer Attempt 1 out of 2

Question Watch Video Show Examples
If using the method of completing the square to solve the quadratic equation $x^{2}+8 x+37=0$ , which number would have to be added to "complete the square"? Answer Attempt 1 out of 2

Solve for $k$ . $36 k^{2}-13 k+1=0$
Write each solution as an integer, proper fraction, or improper fraction in simplest form. If there are multiple solutions, separate them with commas. $k=$ $\square$

Find the $x$ -intercepts of the parabola with vertex $(6,27)$ and $y$ -intercept $(0,-81)$ . Round to the nearest hundredth.

Find the value of $y$ for the equation $y=-5 x^{2}-10 x-15$ .

Graph the function. Label the $x$ -intercept(s), vertex, and axis of symmetry.
21. $f(x)=(x-3)(x+1)$
22. $h(x)=x(x+6)$

Factor each quadratic expression. (10) $x^{2}+5 x+6$ (12) $x^{2}-5 x+4$ $13 x^{2}-4 x-12$

Solve the equation by factoring. Check your solution. If there are multiple solutions, list the solutions from least to greatest separated by a comma. Leave in simplest fractional form. $2 x^{2}-x-3=0$ $\square$

Find the $x$ -intercepts of the parabola with vertex $(1,245)$ and $y$ -intercept $(0,240)$ . Round to the nearest hundredth.

Solve the inequality $2x - 8 \geq -3x^2$ and express the solution in interval notation.

Find $x$ such that $f(x)=0$ for $f(x)=x^{2}-6x+9$ . Options: A) -3 B) 0 C) 3 D) 9

Find the equivalent expression for $2 x^{2}-14 x+24$ from the options: A, B, C, D.

Find the solutions to $2 x^{2} = -10 x + 12$ . Select from: $x=1, x=6, x=-3, x=-6, x=-2, x=3$ .

Find the solutions for $2 x^{2} = -10 x + 12$ . Choose from: $x=1$ , $x=6$ , $x=-3$ , $x=-6$ , $x=-2$ , $x=3$ .

Find the $y$ -intercept of the quadratic function $f(x)=a(x-p)(x-q)$ using $a$ , $p$ , and $q$ .

Solve the equation $e^{2}+6 e+8=0$ .

Solve the equation $g^{2}+8g+7=0$ .

Solve the quadratic equation: $k^{2}+10k+16=0$ .

Solve the equation by factoring. Check your solution. If there are multiple solutions, list the solutions from leas greatest separated by a comma. $x^{2}+4=0$ $\square$

4) Through: $(2,-1)$ Vertex: $(3,6)$

For the parabola $y=-2 x^{2}+4 x-3$ find the vertex. $(4,-3)$ $(1,-1)$ $(-1,1)$ $(-3,4)$

Find the discriminant of the equation $5 x^{2}+7 x+3=0$ . 28 34 $-11$ $-53$

Exponents and Polymomials Factoring a quadratic with leading coefficient greater than 1
Factor. $5 z^{2}-18 z-8$

Q Exponents and Polynomials Factoring a quadratic with leading coefficient greater than 1
Factor. $8 x^{2}+18 x+9$ $\square$

侪 $\sqrt{2}$ Write the equation in standard form for the hyperbola $-2 x^{2}+y^{2}+12 y-32=0$ $\square$ 믐 () 2 Submit

15. What are the solutions for the quadratic function $y=3 x^{2}-8 x+7$ ? $x=\frac{4 \pm i \sqrt{5}}{3}$ $x=\frac{-4 \pm i \sqrt{5}}{3}$ $x=-6 ; x=14$ $x=\frac{8 \pm \sqrt{20}}{6}$

Quadratic Formula
Solve for x . $\begin{array}{c} x^{2}-5 x-24=0 \\ x=[?] \end{array}$
Remember the quadratic formula: $x=\frac{-b \pm \sqrt{b^{2}-4 a c}}{2 a}$

atic by factoring. $2 x^{2}+9 x-1=2 x-7$

If the range of a quadratic function is $5 \leq y<\infty$ , which of the following could be true? None of these are correct. The parabola has a maximum at $(2,5)$ . The parabola has a minimum at $(2,1)$ . The parabola has a maximum at $(5,1)$ .

a) Factorise $x^{2}+9 x+14$ . b) By sketching a graph, solve the inequality $x^{2}+9 x+14 \leq 0$ .

How many zeros does $f(x)=a(x-5)^{2}$ have if $a<0$ ? 1) It is impossible to determine. 2) 1 3) 0 4) 2

What are the solutions to $100 x^{2}-1=0$ ? Use the keypad to enter your answers in the boxes. Find more symbols by using the drop-down arrow at the top of the keypad.
The solutions to the quadratic equation are $x=$ $\square$ and $x=$ $\square$

Solve using the quadratic formula. $k^{2}-k-4=0$
Write your answers as integers, proper or improper fractions in simplest form, or decimals rounded to the nearest hundredth. $k=$ $\square$ or $k=$ $\square$ Submit

Solve using the quadratic formula. $-2 t^{2}+9 t+7=0$
Write your answers as integers, proper or improper fractions in simplest form, or decimals rounded to the nearest hundredth. $t=$ $\square$ or $t=$ $\square$

6. Untersuchung von Funktionenscharen
Untersuchen Sie die Schar $f_{a}$ auf Nullstellen und Extrema. Zeichnen Sie $f_{a}$ . Es gelte $a>0$ . a) $f_{a}(x)=-\frac{1}{a} x^{2}+a x$ ,

Solve for $y$ . $y^{2}-6 y+8=0$

Solve the equation $(x-1)(x-3)=0$ for the values of $x$ .

Solve the equation: $(x-1)(x-3)=0$

Solve the equation $x^{2}-32=0$ to find $x$ algebraically and graphically.

Graph the function $f(x)=-x^{2}+4x+1$ and find its vertex, max/min, axis of symmetry, intercepts, domain, and range.

Solve the inequality: $9x - 9 \geq -4x^2$ . Provide the solution in interval notation.

Rewrite $f(x)=x^{2}+6 x$ in vertex form and find its roots (i.e. $x$ -intercepts).