Chapter 5

Factor each expression. $$ 25 z^{2}-9 $$

Which term is NOT a common factor of \(4 a^{2} c^{2}+2 a^{2} c-6 a c^{2} ?\) $$ \begin{array}{lllll}{\text { A. } 4 c} & {\text { B. } 2 a} & {\text { C. } 2 a c} & {\text { D. } a c}\end{array} $$

Sketch the graph of \(y=x^{2}-6 x+2 .\) Explain how to identify the vertex and two other points on the parabola.

Use factoring to find all complex solutions to \(x^{4}-16=0 .\) Show your work.

Factor each expression. $$ 6 s^{2}+9 s $$

Find a quadratic model for the values in the table. $$ \begin{array}{|c|c|c|c|c|c|}\hline x & {0} & {5} & {10} & {15} & {20} \\\ \hline y & {17} & {39} & {54} & {61} & {61} \\ \hline\end{array} $$

Solve by completing the square. $$ x^{2}-8 x-20=0 $$

Solve each equation using a graphing calculator. $$ 2 x^{2}+3 x-4=0 $$

State the dimensions of each matrix. Identify the indicated element. $$ \left[\begin{array}{rrr}{4} & {6} & {5} \\ {1} & {-3} & {0} \\ {1} & {1} & {9}\end{array}\right] ; a_{13} $$

What is the factored form of \(4 x^{2}+15 x-4 ?\) A. \((2 x+2)(2 x-2)\) C. \((4 x+1)(x-4)\) B. \((2 x-4)(2 x+1)\) D. \((4 x-1)(x+4)\)

Solve each matrix equation. $$ X+\left[\begin{array}{rr}{0} & {4} \\ {-2} & {1}\end{array}\right]=\left[\begin{array}{ll}{3} & {0} \\ {1} & {1}\end{array}\right] $$

Solve by completing the square. $$ 2 y^{2}=4 y-1 $$

Solve each equation using a graphing calculator. $$ 4 x^{2}+x=1 $$

State the dimensions of each matrix. Identify the indicated element. $$ \left[\begin{array}{rrr}{4} & {-1} & {6} \\ {2} & {0} & {0}\end{array}\right] ; a_{21} $$

Solve each matrix equation. $$ X-\left[\begin{array}{rr}{3} & {3} \\ {-2} & {-1}\end{array}\right]=\left[\begin{array}{ll}{1} & {0} \\ {0} & {1}\end{array}\right] $$

Solve by completing the square. $$ x^{2}-3 x-8=0 $$

Solve each equation using a graphing calculator. $$ x^{2}=-7 x-8 $$

State the dimensions of each matrix. Identify the indicated element. $$ \left[\begin{array}{rrr}{-9} & {1} & {-1} \\ {0} & {6} & {0} \\ {1} & {0} & {-2}\end{array}\right] ; a_{32} $$

Each matrix represents vertices of a polygon. Translate each figure 3 units right and 2 units down. Express your answer as a matrix. $$ \left[\begin{array}{rrr}{2} & {3} & {-1} \\ {-5} & {1} & {0}\end{array}\right] $$

Graph each function. $$ y=-2(x+1)^{2}-3 $$

Name the property of real numbers illustrated by each equation. $$ 3(2 x+y)=6 x+3 y $$

Graph each function. $$ y=\frac{1}{2}(x-4)^{2}+1 $$

Name the property of real numbers illustrated by each equation. $$ 3 x^{2}+7 y=7 y+3 x^{2} $$

Use the following information about quadratic functions for Exercises \(85-90\) . vertex form: \(y=a(x-h)^{2}+k \quad\) standard form: \(y=a x^{2}+b x+c\) When \(y=-3 x^{2}-18 x-23\) is written in vertex form, what is the value of \(k ?\)

Write each function in vertex form. $$ y=x^{2}-2 x+1 $$

Multiply. $$ \left[\begin{array}{rr}{0} & {-3} \\ {-3} & {1}\end{array}\right]\left[\begin{array}{rr}{4} & {0} \\ {-9} & {1}\end{array}\right] $$

Graph each function. $$ y=3(x-1)^{2}-5 $$

Name the property of real numbers illustrated by each equation. $$ 4(3 x)=(4 \cdot 3) x $$

Use the following information about quadratic functions for Exercises \(85-90\) . vertex form: \(y=a(x-h)^{2}+k \quad\) standard form: \(y=a x^{2}+b x+c\) When \(y=2(x-3)(x+5)\) is written in standard form, what is the value of \(b ?\)

Write each function in vertex form. $$ y=-2 x^{2}+2 x+5 $$

Multiply. $$ \left[\begin{array}{cc}{3} & {10} \\ {1} & {5}\end{array}\right]\left[\begin{array}{cc}{-2} & {4} \\ {-1} & {4}\end{array}\right] $$

Graph each point in coordinate space. $$ (2,0,-4) $$

Name the property of real numbers illustrated by each equation. $$ 3+(-3)=0 $$

Use the following information about quadratic functions for Exercises \(85-90\) . vertex form: \(y=a(x-h)^{2}+k \quad\) standard form: \(y=a x^{2}+b x+c\) When \(y=-2(x+3)^{2}+25\) is written in standard form, what is the value of \(c ?\)

Write each function in vertex form. $$ y=5 x^{2}-1 $$

Graph each point in coordinate space. $$ (0,-3,5) $$

Use the following information about quadratic functions for Exercises \(85-90\) . vertex form: \(y=a(x-h)^{2}+k \quad\) standard form: \(y=a x^{2}+b x+c\) For \(y=3 x^{2}-7 x+5,\) what is the \(x\) -value of the vertex? Enter your answer as an improper fraction in simplest form.

Evaluate each determinant. $$ \left|\begin{array}{rrr}{2} & {-1} & {0} \\ {1} & {0} & {3} \\ {4} & {-2} & {1}\end{array}\right| $$

Graph each point in coordinate space. $$ (9,-1,0) $$

Use the following information about quadratic functions for Exercises \(85-90\) . vertex form: \(y=a(x-h)^{2}+k \quad\) standard form: \(y=a x^{2}+b x+c\). What is the \(y\) -coordinate of the vertex of \(y=-2(x+1)^{2}+3 ?\)

Evaluate each determinant. $$ \left|\begin{array}{lll}{1} & {5} & {0} \\ {3} & {3} & {5} \\ {0} & {1} & {2}\end{array}\right| $$

Use the following information about quadratic functions for Exercises \(85-90\) . vertex form: \(y=a(x-h)^{2}+k \quad\) standard form: \(y=a x^{2}+b x+c\). How many units down must you shift the graph of \(y=3(x+3)^{2}\) to get the graph of \(y=3(x+3)^{2}-2 ?\)

Evaluate each determinant. $$ \left|\begin{array}{lll}{0} & {4} & {1} \\ {1} & {0} & {1} \\ {1} & {2} & {1}\end{array}\right| $$

Graph each function. $$ y=x^{2}-5 $$

Coins The combined mass of a penny and a nickel and a dime is 9.8 g. Ten nickels and three pennies have the same mass as 25 dimes. Fifty dimes have the same mass as 18 nickels and 10 pennies. Write and solve a system of equations to find the mass of each type of coin.

Graph each function. $$ y=x^{2}-4 x+8 $$

Graph each function. $$ y=3 x^{2}+6 x+5 $$

Solve each matrix equation. $$ \left[\begin{array}{rr}{0} & {1} \\ {-1} & {2}\end{array}\right] X=\left[\begin{array}{l}{20} \\ {10}\end{array}\right] $$

Solve each matrix equation. $$ \left[\begin{array}{rr}{-1} & {3} \\ {1} & {-2}\end{array}\right] X=\left[\begin{array}{r}{4} \\ {-4}\end{array}\right] $$

Solve each matrix equation. Find the maximum and minimum values of the objective function \(P=2 x+y,\) under the constraints at the right. $$ \left\\{\begin{array}{ll}{y \geq 2 x-2} & {x \geq 0} \\ {y \leq-x+4} & {y \geq 0}\end{array}\right. $$