Chapter 5

Write each quadratic function in vertex form, if not already in that form. Then identify the vertex, axis of symmetry, and direction of opening. $$ y=\frac{1}{3}(x-1)^{2}+2 $$

Simplify. $$ \sqrt{125} $$

Solve each equation by using the Square Root Property. \(x^{2}+12 x+36=5\)

Solve each equation by graphing. If exact roots cannot be found, state the consecutive integers between which the roots are located. $$ -x^{2}+x=-20 $$

Solve each equation by factoring. Then graph. \(x^{2}-3 x-28=0\)

Determine whether each function has a maximum or a minimum value and find the maximum or minimum value. Then state the domain and range of the function. $$ f(x)=3 x^{2} $$

Complete parts a–c for each quadratic equation. a. Find the value of the discriminant. b. Describe the number and type of roots. c. Find the exact solutions by using the Quadratic Formula. \(x^{2}-2 x+5=0\)

Solve each inequality using a graph, a table, or algebraically. $$ x^{2}-4 x \leq 5 $$

Write each quadratic function in vertex form, if not already in that form. Then identify the vertex, axis of symmetry, and direction of opening. $$ y=-x^{2}-4 x+8 $$

Simplify. $$ \sqrt{147} $$

Solve each equation by using the Square Root Property. \(x^{2}-3 x+\frac{9}{4}=6\)

Solve each equation by graphing. If exact roots cannot be found, state the consecutive integers between which the roots are located. $$ x^{2}-9 x=-18 $$

Solve each equation by factoring. Then graph. \(x^{2}=25\)

Determine whether each function has a maximum or a minimum value and find the maximum or minimum value. Then state the domain and range of the function. $$ f(x)=-x^{2}-9 $$

Complete parts a–c for each quadratic equation. a. Find the value of the discriminant. b. Describe the number and type of roots. c. Find the exact solutions by using the Quadratic Formula. \(x^{2}-x+6=0\)

Solve each inequality using a graph, a table, or algebraically. $$ x^{2}+2 x \geq 24 $$

Write each quadratic function in vertex form, if not already in that form. Then identify the vertex, axis of symmetry, and direction of opening. $$ y=x^{2}-6 x+1 $$

Simplify. $$ \sqrt{\frac{192}{121}} $$

Find the value of c that makes each trinomial a perfect square. Then write the trinomial as a perfect square. \(x^{2}+16 x+c\)

Solve each equation by graphing. If exact roots cannot be found, state the consecutive integers between which the roots are located. $$ 14 x+x^{2}+49=0 $$

Determine whether each function has a maximum or a minimum value and find the maximum or minimum value. Then state the domain and range of the function. $$ f(x)=x^{2}-8 x+2 $$

Solve each equation by using the method of your choice. Find exact solutions. \(x^{2}-30 x-64=0\)

Solve each inequality using a graph, a table, or algebraically. $$ -x^{2}-x+12 \geq 0 $$

Write each quadratic function in vertex form, if not already in that form. Then identify the vertex, axis of symmetry, and direction of opening. $$ y=5 x^{2}-6 $$

Simplify. $$ \sqrt{\frac{350}{81}} $$

Find the value of c that makes each trinomial a perfect square. Then write the trinomial as a perfect square. \(x^{2}-18 x+c\)

Solve each equation by graphing. If exact roots cannot be found, state the consecutive integers between which the roots are located. $$ -12 x+x^{2}=-36 $$

Solve each equation by factoring. Then graph. \(x^{2}+3 x=18\)

Determine whether each function has a maximum or a minimum value and find the maximum or minimum value. Then state the domain and range of the function. $$ f(x)=x^{2}+6 x-2 $$

Solve each equation by using the method of your choice. Find exact solutions. \(7 x^{2}+3=0\)

Solve each inequality using a graph, a table, or algebraically. $$ -x^{2}-6 x+7 \leq 0 $$

Write each quadratic function in vertex form, if not already in that form. Then identify the vertex, axis of symmetry, and direction of opening. $$ y=-8 x^{2}+3 $$

Simplify. $$ \sqrt{-144} $$

Find the value of c that makes each trinomial a perfect square. Then write the trinomial as a perfect square. \(x^{2}-15 x+c\)

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

Solve each equation by factoring. Then graph. \(x^{2}-4 x=21\)

Determine whether each function has a maximum or a minimum value and find the maximum or minimum value. Then state the domain and range of the function. $$ f(x)=4 x-x^{2}+1 $$

Solve each equation by using the method of your choice. Find exact solutions. \(x^{2}-4 x+7=0\)

LANDSCAPING Kinu wants to plant a garden and surround it with decorative stones. She has enough stones to enclose a rectangular garden with a perimeter of 68 feet, but she wants the garden to cover no more than 240 square feet. What could the width of her garden be?

Simplify. $$ \sqrt{-81} $$

Find the value of c that makes each trinomial a perfect square. Then write the trinomial as a perfect square. \(x^{2}+7 x+c\)

Solve each equation by graphing. If exact roots cannot be found, state the consecutive integers between which the roots are located. $$ -x^{2}+4 x-6=0 $$

Solve each equation by factoring. Then graph. \(-2 x^{2}+12 x-16=0\)

Determine whether each function has a maximum or a minimum value and find the maximum or minimum value. Then state the domain and range of the function. $$ f(x)=3-x^{2}-6 x $$

Solve each equation by using the method of your choice. Find exact solutions. \(2 x^{2}+6 x-3=0\)

GEOMETRY A rectangle is 6 centimeters longer than it is wide. Find the possible dimensions if the area of the rectangle is more than 216 square centimeters.

Simplify. $$ \sqrt{-64 x^{4}} $$

Solve each equation by completing the square. \(x^{2}-8 x+15=0\)

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

Solve each equation by factoring. Then graph. \(-3 x^{2}-6 x+9=0\)