Chapter 9

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

State the meanings of the symbols \(\sqrt{,},-\sqrt{,},\) and \(\pm \sqrt{.}\)

Define the roots of a quadratic equation.

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

What formula can you use to solve any quadratic equation?

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

Is the radical expression in simplest form? Explain. a. \(\frac{3}{5} \sqrt{2}\) b. \(\sqrt{\frac{3}{16}}\) c. \(5 \sqrt{40}\)

How can you use the discriminant to tell the number of solutions of \(a x^{2}+b x+c=0\) and the number of \(x\) -intercepts of the graph of the equation?

Give an example of a perfect square and an example of an irrational number.

Write the steps for solving a quadratic equation using a graph.

Describe the steps you would follow to decide which of the three basic models best fits a collection of data.

Describe the steps used to sketch the graph of a quadratic inequality.

Explain how to use the quadratic formula to solve \(-2 x^{2}+5 x=-7\).

Why is the vertical line that passes through the vertex of a parabola called the axis of symmetry?

Explain how to use the product property of radicals to simplify \(\sqrt{3} \cdot \sqrt{15}\)

Find the discriminant for the equation. Then tell if the equation has two solutions, one solution, or no real solution. $$3 x^{2}-2 x+5=0$$

Explain how to find solutions of an equation of the form \(a x^{2}+c=0\)

Is \((0,3)\) inside or outside the graph of \(y=x^{2}+3 x+2 ?\)

Explain how you can decide whether the graph of \(y=3 x^{2}+2 x-4\) opens up or down.

Explain how to use the quotient property of radicals to simplify \(\sqrt{\frac{4}{25}}\)

Find the discriminant for the equation. Then tell if the equation has two solutions, one solution, or no real solution. $$-3 x^{2}+6 x-3=0$$

Use the quadratic formula to solve the equation. $$x^{2}+6 x-7=0$$

Find the coordinates of the vertex of the graph of \(y=2 x^{2}+4 x-2\)

Find the discriminant for the equation. Then tell if the equation has two solutions, one solution, or no real solution. $$x^{2}-5 x-10=0$$

Use the quadratic formula to solve the equation. $$x^{2}-2 x-15=0$$

Tell whether the graph opens up or down. Write an equation of the axis of symmetry. $$ y=x^{2}+4 x-1 $$

Match the radical expression with its simplified form. A. \(3 \sqrt{6}\) B. \(9 \sqrt{6}\) C. \(2 \sqrt{2}\) D. \(4 \sqrt{2}\) $$\sqrt{54}$$

Solve the equation algebraically. Check the solution graphically. $$ 3 x^{2}=12 $$

Use the data: \((0,1),(1,1.25),(2,2),(3,3.25),(4,5),(5,7.25)\) Draw a scatter plot of the data.

Use the quadratic formula to solve the equation. $$x^{2}+12 x+36=0$$

Tell whether the graph opens up or down. Write an equation of the axis of symmetry. $$ y=3 x^{2}+8 x-6 $$

Solve the equation algebraically. Check the solution graphically. $$ 4 x^{2}=16 $$

Use the data: \((0,1),(1,1.25),(2,2),(3,3.25),(4,5),(5,7.25)\) Decide which type of model best fits the data. Explain your reasoning.

Use the quadratic formula to solve the equation. $$4 x^{2}-8 x+3=0$$

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

Tell whether the graph opens up or down. Write an equation of the axis of symmetry. $$ y=x^{2}+7 x-1 $$

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

Solve the equation algebraically. Check the solution graphically. $$ 5 x^{2}=125 $$

Use the data: \((0,1),(1,1.25),(2,2),(3,3.25),(4,5),(5,7.25)\) Write a model that fits the data.

Use the quadratic formula to solve the equation. $$3 x^{2}+x-1=0$$

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

Tell whether the graph opens up or down. Write an equation of the axis of symmetry. $$ y=-x^{2}-4 x+2 $$

Using THE DISCRIMINANT Tell if the equation has two solutions, one solution, or no real solution. $$x^{2}-3 x+2=0$$

Evaluate the expression. $$\sqrt{0.81}$$

Solve the equation algebraically. Check the solution graphically. $$ 3 x^{2}=27 $$

Make a scatter plot of the data. Then name the type of model that best fits the data. $$(-1,-6),(-3,4),(2,9),(-2,-3),(0,-5),(1,0)$$

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

Sketch the graph of the inequality. $$y

Tell whether the graph opens up or down. Write an equation of the axis of symmetry. $$ y=5 x^{2}-2 x+4 $$

Describe the error.Simplify correctly. $$\begin{aligned} &\sqrt{50}=\sqrt{5}+70\\\ &r=5 \sqrt{10} \end{aligned}$$