Chapter 9

Solve the equation algebraically. Check your solutions by graphing. $$-2 x^{2}=-18$$

Use the quadratic formula to solve the equation. Write your solutions in simplest form. $$x^{2}-2 x-15=0$$

Match the radical expression with its simplest form. $$ \sqrt{54} $$ A. \(3 \sqrt{6}\) B. \(5 \sqrt{3}\) C. \(7 \sqrt{2}\) D. \(3 \sqrt{5}\)

Determine the number of real solutions for each equation. $$ x^{2}+2=-2 $$

Determine whether each expression is rational or irrational. $$ \sqrt{25} $$

Sketch the graph of the inequality. $$ y \leq x^{2} $$

Sketch the graph of the function. Label the coordinates of the vertex. Write an equation for the axis of symmetry. $$ y=-3 x^{2} $$

Estimate the solutions of the equation by graphing. Check your solutions algebraically. $$3 x^{2}=48$$

Use the quadratic formula to solve the equation. Write your solutions in simplest form. $$x^{2}+12 x+36=0$$

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

Solve the equation or write no real solution. $$ y^{2}=49 $$

Determine whether each expression is rational or irrational. $$ \sqrt{6} $$

Sketch the graph of the inequality. $$ y>-x^{2}+3 $$

Sketch the graph of the function. Label the coordinates of the vertex. Write an equation for the axis of symmetry. $$ y=-5 x^{2}+10 $$

Estimate the solutions of the equation by graphing. Check your solutions algebraically. $$x^{2}-4=5$$

Use the quadratic formula to solve the equation. Write your solutions in simplest form. $$4 x^{2}-8 x+3=0$$

Determine whether the graph of the function will intersect the x-axis in zero, one, or two points. \(y=x^{2}+2 x+4\)

Simplify the expression. $$ \sqrt{24} $$

Solve the equation or write no real solution. $$ x^{2}=-16 $$

Determine whether each expression is rational or irrational. $$ \sqrt{100} $$

Sketch the graph of the inequality. $$ y<-x^{2}+2 x $$

Sketch the graph of the function. Label the coordinates of the vertex. Write an equation for the axis of symmetry. $$ y=x^{2}+4 $$

Estimate the solutions of the equation by graphing. Check your solutions algebraically. $$-x^{2}+7 x-10=0$$

Use the quadratic formula to solve the equation. Write your solutions in simplest form. $$3 x^{2}+x-1=0$$

Determine whether the graph of the function will intersect the x-axis in zero, one, or two points. \(y=-x^{2}-3 x+5\)

Simplify the expression. $$ \sqrt{60} $$

Solve the equation or write no real solution. $$ n^{2}=7 $$

Determine whether each expression is rational or irrational. $$ \sqrt{10} $$

Sketch the graph of the inequality. $$ y \geq x^{2}-2 x $$

Sketch the graph of the function. Label the coordinates of the vertex. Write an equation for the axis of symmetry. $$ y=x^{2}-6 x+8 $$

Use the quadratic formula to solve the equation. Write your solutions in simplest form. $$x^{2}+6 x-3=0$$

Determine whether the graph of the function will intersect the x-axis in zero, one, or two points. \(y=6 x-3-3 x^{2}\)

Simplify the expression. $$ \sqrt{\frac{64}{25}} $$

Solve the equation or write no real solution. $$ 3 x^{2}-20=-2 $$

Use a calculator or a table of square roots to evaluate the expression. Round the results to the nearest hundredth. $$ 1 \pm \sqrt{2} $$

Sketch the graph of the inequality. $$ y<-2 x^{2}+6 x $$

Sketch the graph of the function. Label the coordinates of the vertex. Write an equation for the axis of symmetry. $$ y=-3 x^{2}+6 x+2 $$

Write the quadratic equation in standard form. $$x^{2}-6 x=-6$$

Write the equation in standard form. Then use the quadratic formula to solve the equation. $$2 x^{2}=-x+6$$

Find the discriminant of the quadratic equation. \(-2 x^{2}-5 x+3=0\)

Simplify the expression. $$ \sqrt{\frac{15}{16}} $$

Solve the equation or write no real solution. $$ 5 x^{2}=-25 $$

Use a calculator or a table of square roots to evaluate the expression. Round the results to the nearest hundredth. $$ 6 \pm 5 \sqrt{3} $$

Sketch the graph of the inequality. $$ y \leq 2 x^{2}-4 x+3 $$

Sketch the graph of the function. Label the coordinates of the vertex. Write an equation for the axis of symmetry. $$ y=2 x^{2}-8 x+3 $$

Write the quadratic equation in standard form. $$-x^{2}=15$$

Write the equation in standard form. Then use the quadratic formula to solve the equation. $$-3 x=2 x^{2}+1$$

Find the discriminant of the quadratic equation. \(3 x^{2}+6 x-8=0\)

Simplify the expression. $$ \frac{1}{2} \sqrt{20} $$

Solve the equation or write no real solution. $$ 2 x^{2}-8=0 $$