Chapter 5

Solve each equation by graphing. If exact roots cannot be found, state the consecutive integers between which the roots are located. \(0=-x^{2}-4 x+5\)

FUND-RAISING For Exercises 56 and 57 , use the following information. Last year, 300 people attended the Sunnybrook High School Drama Club's winter play. The ticket price was \(\$ 8 .\) The advisor estimates that 20 fewer people would attend for each \(\$ 1\) increase in ticket price. What ticket price would give the most income for the Drama Club?

Solve each equation by using the Square Root Property. \(x^{2}-8 x+16=7\)

Solve each equation by using the method of your choice. Find exact solutions. $$ 3 x^{2}+6 x-2=3 $$

CHALLENGE Explain how you can find an equation of a parabola using the coordinates of three points on its graph.

Simplify. $$ (3-5 i)+(3+5 i) $$

Evaluate the determinant of each matrix. $$ \left[\begin{array}{rrr}{2} & {-1} & {-6} \\ {5} & {0} & {3} \\ {-3} & {2} & {11}\end{array}\right] $$

Solve each equation by graphing. If exact roots cannot be found, state the consecutive integers between which the roots are located. \(0=4 x^{2}+4 x+1\)

FUND-RAISING For Exercises 56 and 57 , use the following information. Last year, 300 people attended the Sunnybrook High School Drama Club's winter play. The ticket price was \(\$ 8 .\) The advisor estimates that 20 fewer people would attend for each \(\$ 1\) increase in ticket price. If the Drama Club raised its tickets to this price, how much income should it expect to bring in?

Solve each equation by using the Square Root Property. \(4 x^{2}-4 x+1=8\)

Solve each matrix equation or system of equations by using inverse matrices. $$ \left[\begin{array}{rr}{3} & {6} \\ {2} & {-1}\end{array}\right] \cdot\left[\begin{array}{l}{a} \\\ {b}\end{array}\right]=\left[\begin{array}{c}{-3} \\ {18}\end{array}\right] $$

Simplify. $$ (7-4 i)-(3+i) $$

Evaluate the determinant of each matrix. $$ \left[\begin{array}{rrr}{6} & {5} & {2} \\ {-3} & {0} & {-6} \\ {1} & {4} & {2}\end{array}\right] $$

Solve each equation by graphing. If exact roots cannot be found, state the consecutive integers between which the roots are located. \(0=3 x^{2}-10 x-4\)

Find the value of the maximum or minimum of each quadratic function to the nearest hundredth. $$ f(x)=3 x^{2}-7 x+2 $$

Simplify. \(\frac{2 i}{3+i}\)

Solve each matrix equation or system of equations by using inverse matrices. $$ \left[\begin{array}{rr}{5} & {-7} \\ {-3} & {4}\end{array}\right] \cdot\left[\begin{array}{c}{m} \\\ {n}\end{array}\right]=\left[\begin{array}{r}{-1} \\ {1}\end{array}\right] $$

ACT/SAT If \(f(x)=x^{2}-5 x\) and \(f(n)=-4\) which of the following could be \(n ?\) \(\mathrm{A}-5\) \(\mathrm{B}-4\) \(\mathrm{C}-1\) \(\mathrm{D} 1\)

Simplify. $$ (-3-i)(2-2 i) $$

Use the Internet or other reference to find examples of the golden rectangle in architecture. What applications does the golden ratio have in music?

Determine whether \(f(x)=3 x^{2}-12 x-7\) has a maximum or a minimum value. Then find the maximum or minimum value.

Find the value of the maximum or minimum of each quadratic function to the nearest hundredth. $$ f(x)=-5 x^{2}+8 x $$

Simplify. \(\frac{4}{5-i}\)

Solve each matrix equation or system of equations by using inverse matrices. $$ \begin{array}{l}{3 j+2 k=8} \\ {j-7 k=18}\end{array} $$

REVIEW Which of the following most accurately describes the translation of the graph of \(y=(x+5)^{2}-1\) to the graph of \(y=(x-1)^{2}+3 ?\) \(\mathbf{F}\) up 4 and 6 to the right \(\mathbf{G}\) up 4 and 1 to the left \(\mathbf{H}\) down 1 and 1 to the right \(\mathbf{J}\) down 1 and 5 to the left

Simplify. $$ \frac{(10+i)^{2}}{4-i} $$

Factor completely. $$ x^{2}+5 x $$

Vince needs 12 quarts of a 60% anti-freeze solution. He will combine an amount of 100% anti-freeze with an amount of a 50% anti-freeze solution. How many quarts of each solution should be mixed to make the required amount of the 60% anti-freeze solution?

Find the value of the maximum or minimum of each quadratic function to the nearest hundredth. $$ f(x)=2 x^{2}-3 x+2 $$

Simplify. \(\frac{1+i}{3-2 i}\)

Solve each matrix equation or system of equations by using inverse matrices. $$ \begin{array}{l}{5 y+2 z=11} \\ {10 y-4 z=-2}\end{array} $$

Find the value of the discriminant for each quadratic equation. Then describe the number and type of roots for the equation. $$ 3 x^{2}-6 x+2=0 $$

Simplify. $$ \frac{2-i}{3-4 i} $$

Factor completely. $$ x^{2}-100 $$

Write a perfect square trinomial equation in which the linear coefficient is negative and the constant term is a fraction. Then solve the equation.

Find the value of the maximum or minimum of each quadratic function to the nearest hundredth. $$ f(x)=-6 x^{2}+9 x $$

Solve each system of inequalities. \(x+y \leq 9\) \(x-y \leq 3\) \(y-x \geq 4\)

Find each product, if possible. $$ \left[\begin{array}{rr}{-6} & {3} \\ {4} & {7}\end{array}\right] \cdot\left[\begin{array}{rr}{2} & {-5} \\ {-3} & {6}\end{array}\right] $$

Find the value of the discriminant for each quadratic equation. Then describe the number and type of roots for the equation. $$ 4 x^{2}+7 x=11 $$

Simplify. $$ (-5+2 i)(6-i)(4+3 i) $$

Factor completely. $$ x^{2}-11 x+28 $$

Find the value of the maximum or minimum of each quadratic function to the nearest hundredth. $$ f(x)=7 x^{2}+4 x+1 $$

Solve each system of inequalities. \(x \geq 1\) \(y \leq-1\) \(y \leq x\)

Find each product, if possible. $$ \left[\begin{array}{ccc}{2} & {-6} & {3}\end{array}\right] \cdot\left[\begin{array}{rr}{3} & {-3} \\ {9} & {0} \\ {-2} & {4}\end{array}\right] $$

Find the value of the discriminant for each quadratic equation. Then describe the number and type of roots for the equation. $$ 2 x^{2}-5 x+6=0 $$

Simplify. $$ (2+i)(1+2 i)(3-4 i) $$

Factor completely. $$ x^{2}-18 x+81 $$

Determine whether the value of \(c\) that makes \(a x^{2}+b x+c\) a perfect square trinomial is sometimes, always, or never negative. Explain your reasoning.

Name the property illustrated by each equation. \(2 x+4 y+3 z=2 x+3 z+4 y\)

Find the value of the maximum or minimum of each quadratic function to the nearest hundredth. $$ f(x)=-4 x^{2}+5 x $$