Chapter 5

For each function, the vertex of the function's graph is given. Find \(c .\) $$ y=x^{2}-6 x+c ;(3,-4) $$

Find the value of \(k\) that would make the left side of each equation a perfect square trinomial. $$ 25 x^{2}-k x+1=0 $$

Solve each equation using any method. When necessary, round real solutions to the nearest hundredth. For imaginary solutions, write exact solutions. $$ x^{2}-2 x+2=0 $$

Solve each equation. Check your answers. $$ x^{2}+36=0 $$

Solve each equation by factoring, by taking square roots, or by graphing. If necessary, round your answer to the nearest hundredth. $$ 12 x^{2}-154=0 $$

Write the equation of each parabola in vertex form. vertex \((-3,6),\) point \((1,-2)\)

Factor each expression. $$ 9 x^{2}-1 $$

The vertex of a parabola is \((3,2)\) . A second point on the parabola is \((1,7)\) . Which point is also on the parabola? F. \((-1,7)\) G. \((3,7)\) H. \((5,7)\) J. \((3,-2)\)

For each function, the vertex of the function's graph is given. Find \(c .\) $$ y=-3 x^{2}+6 x+c ;(1,0) $$

Find the value of \(k\) that would make the left side of each equation a perfect square trinomial. $$ x^{2}+k x+\frac{1}{4}=0 $$

Solve each equation using any method. When necessary, round real solutions to the nearest hundredth. For imaginary solutions, write exact solutions. $$ x^{2}-3 x-8=0 $$

Solve each equation. Check your answers. $$ -5 x^{2}-3=0 $$

Solve each equation by factoring, by taking square roots, or by graphing. If necessary, round your answer to the nearest hundredth. $$ x^{2}+4 x=0 $$

Write the equation of each parabola in vertex form. vertex \((-2,6), y\) -intercept 12

The graph of a quadratic function has vertex \((-3,-2) .\) What is the axis of symmetry? $$\begin{array}{llll}{\text { A. } x=-3} & {\text { B. } x=3} & {\text { c. } y=-2} & {\text { D. } y=2}\end{array}$$

For each function, the vertex of the function's graph is given. Find \(c .\) $$ y=x^{2}+10 x+c ;(-5,-27) $$

Find the value of \(k\) that would make the left side of each equation a perfect square trinomial. $$ 9 x^{2}-k x+4=0 $$

Solve each equation using any method. When necessary, round real solutions to the nearest hundredth. For imaginary solutions, write exact solutions. $$ -3 x^{2}+147=0 $$

Find the first three output values of each fractal-generating function. Use \(z=0\) as the first input value. $$ z^{2}-i $$

Solve each equation by factoring, by taking square roots, or by graphing. If necessary, round your answer to the nearest hundredth. $$ x^{2}=8 x-7 $$

The area in square centimeters of a square mat is \(25 x^{2}-10 x+1 .\) Find the dimensions of the mat in terms of \(x .\)

Which function is NOT a quadratic function? F. \(y=(x-1)(x-2)\) H. \(y=3 x-x^{2}\) G. \(y=x^{2}+2 x-3\) J. \(y=-x^{2}+x(x-3)\)

For each function, the vertex of the function's graph is given. Find \(c .\) $$ y=c-x^{2}-2 x ;(-1,3) $$

Find the value of \(k\) that would make the left side of each equation a perfect square trinomial. $$ 36 x^{2}-k x+1=0 $$

Solve each equation using any method. When necessary, round real solutions to the nearest hundredth. For imaginary solutions, write exact solutions. $$ x^{2}+8 x=4 $$

Find the first three output values of each fractal-generating function. Use \(z=0\) as the first input value. $$ f(z)=z^{2}-2 i $$

Solve each equation by factoring, by taking square roots, or by graphing. If necessary, round your answer to the nearest hundredth. $$ x^{2}+2 x=15 $$

Write the equation of each parabola in vertex form. vertex \((0,5),\) point \((1,-2)\)

The area of a rectangular cloth is \(\left(6 x^{2}-19 x-85\right) \mathrm{cm}^{2}\) . The length is \((2 x+5) \mathrm{cm} .\) Find the width.

What is the quadratic function with a graph that includes \((1,6),(2,11),\) and \((3,20) ?\) Find the function by writing and solving a system of equations. Write the function in standard form. Show all your work.

Solve each equation using any method. When necessary, round real solutions to the nearest hundredth. For imaginary solutions, write exact solutions. $$ x^{2}=6 x-11 $$

Find the first three output values of each fractal-generating function. Use \(z=0\) as the first input value. $$ f(z)=z^{2}+1-i $$

Solve each equation by factoring, by taking square roots, or by graphing. If necessary, round your answer to the nearest hundredth. $$ x^{2}+11 x+10=0 $$

Write the augmented matrix for each system. Then solve the system. $$ \left\\{\begin{array}{l}{3 x-y=7} \\ {2 x+2 y=10}\end{array}\right. $$

Solve each equation using any method. When necessary, round real solutions to the nearest hundredth. For imaginary solutions, write exact solutions. $$ 4 x^{2}-4 x-3=0 $$

Solve each equation. $$ x^{2}+16=-49 $$

Solve each equation by factoring, by taking square roots, or by graphing. If necessary, round your answer to the nearest hundredth. $$ 4 x^{2}+4 x=3 $$

Write the equation of each parabola in vertex form. \(\operatorname{vertex}\left(\frac{1}{4},-\frac{3}{2}\right), \operatorname{point}(1,3)\)

Write the augmented matrix for each system. Then solve the system. $$ \left\\{\begin{aligned} 3 x+y-2 z &=-3 \\ x-3 y-z &=-2 \\ 2 x+2 y+3 z &=11 \end{aligned}\right. $$

Find the quadratic function \(y=a x^{2}+c\) with a graph that has the given points. $$ \left(2, \frac{5}{2}\right),\left(0,-\frac{1}{2}\right) $$

Solve each quadratic equation by completing the square. $$ \frac{1}{3} x^{2}+8 x-3=0 $$

Solve each equation using any method. When necessary, round real solutions to the nearest hundredth. For imaginary solutions, write exact solutions. $$ \frac{x-3}{2}=\frac{6}{x-2} $$

Solve each equation. $$ x^{2}-30=-79 $$

Solve each equation by factoring, by taking square roots, or by graphing. If necessary, round your answer to the nearest hundredth. $$ (x+3)^{2}=9 $$

Write each function in standard form. $$ y=(5 x+6)^{2}-9 $$

Factor each expression completely. $$ 9 x^{2}-36 $$

Find each product. $$ \left[\begin{array}{cc}{2} & {-3}\end{array}\right]\left[\begin{array}{rrrr}{3} & {-2} & {4} & {1} \\ {2} & {0} & {-3} & {2}\end{array}\right] $$

Solve each quadratic equation by completing the square. $$ \frac{1}{2} x^{2}+4 x=2 $$

Solve each equation using any method. When necessary, round real solutions to the nearest hundredth. For imaginary solutions, write exact solutions. $$ \frac{x+2}{5}=\frac{3}{x+1} $$

Solve each equation. $$ 3 x^{2}+1=x^{2}-1 $$