Chapter 9

Use the quadratic formula to solve the equation. $$4 x^{2}-13 x+3=0$$

Simplify the expression. $$5 \sqrt{\frac{6}{2}}$$

Complete these steps for the function. a. Tell whether the graph of the function opens up or down. b. Find the coordinates of the vertex. c. Write an equation of the axis of symmetry. $$ y=6 x^{2}+2 x+4 $$

LOGICAL REASONING Consider the equation \(a x^{2}+b x+c=0\) and use the quadratic formula to justify the statement. If \(b^{2}-4 a c\) is zero, then the equation has one solution.

Evaluate the expression. Give the exact value if possible. Otherwise, approximate to the nearest hundredth. $$\sqrt{13}$$

List the terms of the expression. $$-3+x$$

Represent the solution graphically. Check the solution algebraically. $$ x^{2}-x=6 $$

Use the quadratic formula to solve the equation. $$y^{2}+11 y+10=0$$

Simplify the expression. $$8 \sqrt{\frac{20}{4}}$$

Complete these steps for the function. a. Tell whether the graph of the function opens up or down. b. Find the coordinates of the vertex. c. Write an equation of the axis of symmetry. $$ y=5 x^{2}+10 x+7 $$

LOGICAL REASONING Consider the equation \(a x^{2}+b x+c=0\) and use the quadratic formula to justify the statement. If \(b^{2}-4 a c\) is negative, then the equation has no real solution.

Evaluate the expression. Give the exact value if possible. Otherwise, approximate to the nearest hundredth. $$-\sqrt{125}$$

List the terms of the expression. $$a-5$$

Represent the solution graphically. Check the solution algebraically. $$ x^{2}+2 x=3 $$

Use the quadratic formula to solve the equation. $$7 x^{2}+8 x+1=0$$

Simplify the expression. $$\frac{\sqrt{32}}{\sqrt{25}}$$

Complete these steps for the function. a. Tell whether the graph of the function opens up or down. b. Find the coordinates of the vertex. c. Write an equation of the axis of symmetry. $$ y=-4 x^{2}-4 x+8 $$

GRAPHING FUNCTIONS Graph the function. $$f(x)=-x+1$$

Evaluate the expression. Give the exact value if possible. Otherwise, approximate to the nearest hundredth. $$\sqrt{0.04}$$

List the terms of the expression. $$-5-8 x$$

Use the quadratic formula to solve the equation. $$-3 y^{2}+2 y+8=0$$

Represent the solution graphically. Check the solution algebraically. $$ -x^{2}+x=-2 $$

Simplify the expression. $$\sqrt{\frac{27}{36}}$$

Complete these steps for the function. a. Tell whether the graph of the function opens up or down. b. Find the coordinates of the vertex. c. Write an equation of the axis of symmetry. $$ y=2 x^{2}-7 x-8 $$

GRAPHING FUNCTIONS Graph the function. $$f(x)=-6 x+1$$

Evaluate the expression. Give the exact value if possible. Otherwise, approximate to the nearest hundredth. $$\pm \sqrt{0.75}$$

List the terms of the expression. $$-4 r+s-1$$

Use the quadratic formula to solve the equation. $$6 n^{2}-10 n+3=0$$

Represent the solution graphically. Check the solution algebraically. $$ -x^{2}+3 x=-4 $$

Simplify the expression. $$\frac{\sqrt{49}}{\sqrt{4}}$$

Complete these steps for the function. a. Tell whether the graph of the function opens up or down. b. Find the coordinates of the vertex. c. Write an equation of the axis of symmetry. $$ y=2 x^{2}+7 x-21 $$

GRAPHING FUNCTIONS Graph the function. $$f(x)=3 x-9$$

Evaluate the expression. Give the exact value if possible. Otherwise, approximate to the nearest hundredth. $$-\sqrt{0.1}$$

Simplify the variable expression. $$-(-5)(y)(-y)$$

Use the quadratic formula to solve the equation. $$9 x^{2}+14 x+3=0$$

Represent the solution graphically. Check the solution algebraically. $$ 2 x^{2}+4 x=6 $$

Simplify the expression. $$\frac{\sqrt{36}}{\sqrt{9}}$$

Complete these steps for the function. a. Tell whether the graph of the function opens up or down. b. Find the coordinates of the vertex. c. Write an equation of the axis of symmetry. $$ y=-x^{2}+8 x+32 $$

SOLVING INEQUALITIES Solve the inequality. $$\frac{x}{6} \leq-2$$

Evaluate the expression. Give the exact value if possible. Otherwise, approximate to the nearest hundredth. $$\pm \sqrt{6.25}$$

List the terms of the expression. $$(-3)^{3}(x)(x)$$

Use the quadratic formula to solve the equation. $$8 m^{2}+6 m-1=0$$

Represent the solution graphically. Check the solution algebraically. $$ 3 x^{2}+3 x=6 $$

Simplify the expression. $$\frac{\sqrt{9}}{\sqrt{49}}$$

Complete these steps for the function. a. Tell whether the graph of the function opens up or down. b. Find the coordinates of the vertex. c. Write an equation of the axis of symmetry. $$ y=\frac{1}{2} x^{2}+3 x-7 $$

SOLVING INEQUALITIES Solve the inequality. $$-\frac{x}{3} \geq 15$$

Evaluate \(\sqrt{b^{2}-4 a c}\) for the given values. $$a=4, b=5, c=1$$

List the terms of the expression. $$(-2)(-r)(-r)(-r)$$

Use the quadratic formula to solve the equation. $$7 x^{2}+2 x-1=0$$

Represent the solution graphically. Check the solution algebraically. $$ x^{2}-4 x-5=0 $$