Chapter 8

After reading this section, write out the answers to these questions. Use complete sentences. How can you use the discriminant to determine if a quadratic polynomial can be factored?

After reading this section, write out the answers to these questions. Use complete sentences. When do you use the even-root property to solve a quadratic equation?

After reading this section, write out the answers to these questions. Use complete sentences. Why don't we usually multiply each side of an inequality by an expression involving a variable?

After reading this section, write out the answers to these questions. Use complete sentences. How many solutions are there to any quadratic equation in the complex number system?

Complete each ordered pair so that it satisfies the given equation. $$f(x)=x^{2} \quad(4, \quad),(\quad, 9)$$

Solve each equation by using the quadratic formula. $$x^{2}-3 x+2=0$$

Complete each ordered pair so that it satisfies the given equation. $$f(x)=-x^{2} \quad(-9, \quad),(\quad,-4)$$

Solve each equation by using the quadratic formula. $$x^{2}-7 x+12=0$$

Complete each ordered pair so that it satisfies the given equation. $$f(x)=x^{2}-x-12 \quad(3, \quad),(\quad, 0)$$

Solve each equation by using the quadratic formula. $$x^{2}+5 x+6=0$$

For each given pair of numbers find a quadratic equation with integral coefficients that has the numbers as its solutions. See Example 1. $$\sqrt{5},-\sqrt{5}$$

Solve each equation by using the quadratic formula. $$x^{2}+4 x+3=0$$

For each given pair of numbers find a quadratic equation with integral coefficients that has the numbers as its solutions. See Example 1. $$-\sqrt{7}, \sqrt{7}$$

Solve each equation by using the quadratic formula. $$y^{2}+y=6$$

Solve each equation by using the quadratic formula. $$m^{2}+2 m=8$$

Determine whether the graph of each quadratic function opens upward or downward. $$f(x)=x^{2}+5$$

Solve each equation by using the quadratic formula. $$-6 z^{2}+7 z+3=0$$

For each given pair of numbers find a quadratic equation with integral coefficients that has the numbers as its solutions. See Example 1. $$i \sqrt{2},-i \sqrt{2}$$

Determine whether the graph of each quadratic function opens upward or downward. $$f(x)=2 x^{2}+x-1$$

Solve each equation by using the quadratic formula. $$-8 q^{2}-2 q+1=0$$

Determine whether the graph of each quadratic function opens upward or downward. $$y=-3 x^{2}+4 x+2$$

Solve each equation by using the quadratic formula. $$4 x^{2}-4 x+1=0$$

Use the even-root property to solve each equation. $$x^{2}=81$$

Determine whether the graph of each quadratic function opens upward or downward. $$y=-x^{2}+3$$

Solve each equation by using the quadratic formula. $$4 x^{2}-12 x+9=0$$

Use the even-root property to solve each equation. $$x^{2}=\frac{9}{4}$$

Determine whether the graph of each quadratic function opens upward or downward. $$f(x)=(-2 x+3)^{2}$$

Solve each equation by using the quadratic formula. $$-9 x^{2}+6 x-1=0$$

Use the even-root property to solve each equation. $$x^{2}=\frac{16}{9}$$

Determine whether the graph of each quadratic function opens upward or downward. $$f(x)=(5-x)^{2}$$

Solve each equation by using the quadratic formula. $$-9 x^{2}+24 x-16=0$$

Use the even-root property to solve each equation. $$a^{2}=32$$

Graph each quadratic function, and state its domain and range. $$f(x)=x^{2}+2$$

Solve each equation by using the quadratic formula. $$9+24 x+16 x^{2}=0$$

Use the even-root property to solve each equation. $$(x-3)^{2}=16$$

Graph each quadratic function, and state its domain and range. $$g(x)=x^{2}-4$$

Solve each equation by using the quadratic formula. $$4+20 x=-25 x^{2}$$

Use the even-root property to solve each equation. $$(x+5)^{2}=4$$

Graph each quadratic function, and state its domain and range. $$y=\frac{1}{2} x^{2}-4$$

Solve each equation by using the quadratic formula. $$v^{2}+8 v+6=0$$

Use the even-root property to solve each equation. $$(z+1)^{2}=5$$

Graph each quadratic function, and state its domain and range. $$y=\frac{1}{3} x^{2}-6$$

Solve each equation by using the quadratic formula. $$p^{2}+6 p+4=0$$

Use the even-root property to solve each equation. $$(a-2)^{2}=8$$

Graph each quadratic function, and state its domain and range. $$f(x)=-2 x^{2}+5$$

Solve each equation by using the quadratic formula. $$-x^{2}-5 x+1=0$$

Use the even-root property to solve each equation. $$\left(w-\frac{3}{2}\right)^{2}=\frac{7}{4}$$

Graph each quadratic function, and state its domain and range. $$g(x)=-x^{2}-1$$

Solve each equation by using the quadratic formula. $$-x^{2}-3 x+5=0$$

Use the even-root property to solve each equation. $$\left(w+\frac{2}{3}\right)^{2}=\frac{5}{9}$$