Chapter 5

Solve each equation by factoring, by taking square roots, or by graphing. If necessary, round your answer to the nearest hundredth. $$ 2 x^{2}-6 x=8 $$

Write each function in standard form. $$ y=-(3 x-4)^{2}+6 $$

Factor each expression completely. $$ 18 z^{2}-8 $$

Find each product. $$ \left[\begin{array}{rr}{3} & {10} \\ {1} & {5}\end{array}\right]\left[\begin{array}{rr}{-7} & {2} \\ {8} & {4}\end{array}\right] $$

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

a. The area of a rectangle is 36 \(\mathrm{in.}^{2} .\) The perimeter of the rectangle is 36 \(\mathrm{in.}\) Write an equation using one variable to find the dimensions of the rectangle. b. Find the dimensions of the rectangle to the nearest hundredth of an inch.

Writing In reality, is it possible for Mr. Milde's average to be an imaginary number? Explain.

Solve each equation by factoring, by taking square roots, or by graphing. If necessary, round your answer to the nearest hundredth. $$ 2 x^{2}+x-28=0 $$

Write each function in standard form. $$ y=2 x(x+7)+8 x $$

Factor each expression completely. $$ 12 y^{2}-75 $$

Solve each system by elimination. $$ \left\\{\begin{array}{c}{x+y=7} \\ {5 x-y=5}\end{array}\right. $$

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

Critical Thinking The graphs of each pair of functions intersect. Find their points of intersection without using a calculator. Hint: Solve as a system using substitution. $$ \begin{array}{l}{y=x^{2}} \\ {y=-\frac{1}{2} x^{2}+\frac{3}{2} x+3}\end{array} $$

Write each function in standard form. $$ y=\frac{1}{2}(x-5)^{2}+5 $$

Factor each expression completely. $$ 64 t^{2}-16 $$

Solve each system by elimination. $$ \left\\{\begin{array}{l}{2 x-3 y=-14} \\ {3 x-y=7}\end{array}\right. $$

A rock club's profit from booking local bands depends on the ticket price. Using past recipts the owners find that the profit \(p\) can be modeled by the function \(p=-15 t^{2}+600 t+50,\) where trepresents the ticket price in dollars. a. What price yields the maximum profit? b. What is the maximum profit? c. Open-Ended What price would you pay to see your favorite local band? How much profit would the club owner make using that ticket price?

Writing Summarize how to use the discriminant to analyze the types of solutions of a quadratic equation.

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

Multiple Choice In a complex number plane, what geometric figure describes the complex numbers with absolute value 10\(?\) $$ \begin{array}{ll}{\text { A square }} & {\text { B circle }} \\ {\text { C line }} & {\text { D two points }}\end{array} $$

Critical Thinking The graphs of each pair of functions intersect. Find their points of intersection without using a calculator. Hint: Solve as a system using substitution. $$ \begin{array}{l}{y=x^{2}-2} \\ {y=3 x^{2}-4 x-2}\end{array} $$

Write each function in standard form. $$ y=-0.1(10 x+20)^{2} $$

Factor each expression completely. $$ 12 x^{2}+36 x+27 $$

Solve each system by elimination. $$ \left\\{\begin{array}{l}{x-3 y=2} \\ {x-2 y=1}\end{array}\right. $$

Solve each quadratic equation by completing the square. $$ x^{2}+\frac{3}{4} x=\frac{1}{2} $$

$$ (x+3 i)(x-3 i)=34 $$

Critical Thinking The graphs of each pair of functions intersect. Find their points of intersection without using a calculator. Hint: Solve as a system using substitution. $$ \begin{array}{l}{y=-x^{2}+x+4} \\ {y=2 x^{2}-6}\end{array} $$

Write each function in standard form. $$ y=(1-4 x)^{2}+1 $$

Factor each expression completely. $$ 16 x^{2}-80 x+100 $$

For each direct variation, find the value of \(y\) when \(x=2\) $$ y=2 \text { when } x=5 $$

Without graphing, tell how many \(x\) -intercepts each function has. $$ y=-2 x^{2}+3 x-1 $$

Solve for \(x\) in terms of \(a\). $$ 2 x^{2}-a x=6 a^{2} $$

Simplify each expression. $$ (8 i)(4 i)(-9 i) $$

Factor each expression completely. $$ 2 a^{2}-16 a+32 $$

Each point lies on a parabola that has its vertex at \((0,1) .\) Write the equation of the parabola. Indicate whether the graph opens up or down. $$ (-3,10) $$

For each direct variation, find the value of \(y\) when \(x=2\) $$ y=1 \text { when } x=4 $$

Without graphing, tell how many \(x\) -intercepts each function has. $$ y=0.25 x^{2}+2 x+4 $$

Solve for \(x\) in terms of \(a\). $$ 3 x^{2}+a x=a^{2} $$

Simplify each expression. $$ (2+\sqrt{-1})+(-3+\sqrt{-16}) $$

Open-Ended Write a quadratic equation with the given solutions. 3 and 5

Writing Describe the family of quadratic functions whose members each have \((3,4)\) as its vertex.

Factor each expression completely. $$ 3 x^{2}-24 x-27 $$

For each direct variation, find the value of \(y\) when \(x=2\) $$ y=-2 \text { when } x=4 $$

Without graphing, tell how many \(x\) -intercepts each function has. $$ y=x^{2}+3 x+5 $$

Solve for \(x\) in terms of \(a\). $$ 2 a^{2} x^{2}-8 a x=-6 $$

Simplify each expression. $$ (4+\sqrt{-9})+(6-\sqrt{-49}) $$

Open-Ended Write a quadratic equation with the given solutions. \(-3\) and 2

Factor each expression completely. $$ 18 b^{2}+24 b-10 $$

Without graphing, tell how many \(x\) -intercepts each function has. $$ y=-x^{2}+3 x+10 $$

Solve for \(x\) in terms of \(a\). $$ 4 a^{2} x^{2}+8 a x+3=0 $$