Chapter 9

Give an example of each of the four types of quadratic inequalities.

Identify the values of \(a, b,\) and \(c\) for the quadratic function in standard form \(y=-5 x^{2}+7 x-4\)

What are the roots of a quadratic equation?

Write the formula that you can use to solve any quadratic equation when \(a \neq 0\) and \(b^{2}-4 a c \geq 0.\)

Write the quadratic formula and circle the part that is the discriminant.

Determine whether the radical expression is in simplest form. Explain. $$ \frac{3}{5} \sqrt{2} $$

Is \(2 x-7=15\) a quadratic equation? Explain why or why not.

Complete: since \((-2)^{2}=4,-2\) is a ____ of 4.

What is the U-shaped graph of a quadratic function called?

Explain how you can use a graph to check the solutions of a quadratic equation.

Describe how you can check the solutions of a quadratic equation by looking at the graph of the related function.

What can the discriminant tell you about a quadratic equation?

Determine whether the radical expression is in simplest form. Explain. $$ \sqrt{\frac{3}{16}} $$

State the meaning of the symbols \(\sqrt,-\sqrt{,}\) and \(\pm \sqrt{\underline{\phantom{xxx}}}\) when applied to apositive number \(n\)

Write \(7 x^{2}=12+3 x\) in standard form. What is the leading coefficient?

Sketch the graph of the equation \(y=x^{2}+2 x-4 .\) Plot the point and determine whether it lies inside or outside the parabola. $$ A(0,0) $$

Decide whether the graph of the quadratic function opens up or down. $$ y=x^{2}+4 x-1 $$

Describe how the graphs of \(y=4 x^{2}, y=4 x^{2}+3,\) and \(y=4 x^{2}-6\) are alike and how they are different.

Determine whether the radical expression is in simplest form. Explain. $$ 5 \sqrt{40} $$

Identify the radicand in the equation \(\sqrt{4}=2\)

Determine the number of real solutions for each equation. $$ x^{2}=6 $$

Sketch the graph of the equation \(y=x^{2}+2 x-4 .\) Plot the point and determine whether it lies inside or outside the parabola. $$ B(-1,3) $$

Decide whether the graph of the quadratic function opens up or down. $$ y=3 x^{2}+8 x+6 $$

Write the equation in standard form. Identify the values of a, b, and c that you would use to solve the equation using the quadratic formula. $$x^{2}=1$$

Use the discriminant to determine whether the quadratic equation has two solutions, one solution, or no real solution. \(3 x^{2}-3 x+5=0\)

Determine whether the radical expression is in simplest form. Explain. $$ \frac{1}{\sqrt{2}} $$

Determine the number of real solutions for each equation. $$ x^{2}=0 $$

Evaluate the expression. $$ \sqrt{81} $$

Sketch the graph of the equation \(y=x^{2}+2 x-4 .\) Plot the point and determine whether it lies inside or outside the parabola. $$ C(2,-2) $$

Decide whether the graph of the quadratic function opens up or down. $$ y=-x^{2}+7 x-3 $$

Write the equation in standard form. Identify the values of a, b, and c that you would use to solve the equation using the quadratic formula. $$16 x-32=2 x^{2}$$

Use the discriminant to determine whether the quadratic equation has two solutions, one solution, or no real solution. \(-3 x^{2}+6 x-3=0\)

Match the radical expression with its simplest form. $$ \sqrt{45} $$ 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. $$ x^{2}=-17 $$

Evaluate the expression. $$ \pm \sqrt{121} $$

Decide whether each labeled ordered pair is a solution of the inequality. $$ y<-x^{2} $$

Decide whether the graph of the quadratic function opens up or down. $$ y=-x^{2}-4 x+2 $$

Solve the equation algebraically. Check your solutions by graphing. $$3 x^{2}-12=0$$

Write the equation in standard form. Identify the values of a, b, and c that you would use to solve the equation using the quadratic formula. $$x^{2}-7 x+42=6 x$$

Use the discriminant to determine whether the quadratic equation has two solutions, one solution, or no real solution. \(x^{2}-5 x-10=0\)

Match the radical expression with its simplest form. $$ \sqrt{98} $$ 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. $$ x^{2}-8=-8 $$

Evaluate the expression. $$ -\sqrt{36} $$

Decide whether the graph of the quadratic function opens up or down. $$ y=5 x^{2}-2 x+4 $$

Solve the equation algebraically. Check your solutions by graphing. $$5 x^{2}-5=0$$

Use the quadratic formula to solve the equation. Write your solutions in simplest form. $$x^{2}+6 x-7=0$$

Match the radical expression with its simplest form. $$ \sqrt{75} $$ 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. $$ x^{2}-15=5 $$

Evaluate the expression. $$ -\sqrt{4} $$

Decide whether the graph of the quadratic function opens up or down. $$ y=-8 x^{2}-4 $$