Chapter 11

Use the quadratic formula to solve each equation. These equations have real number solutions only. $$ m^{2}+5 m-6=0 $$

Write the solution set in interval notation. $$ (x+1)(x+5)>0 $$

Solve. See Example 1. $$ 2 x=\sqrt{10+3 x} $$

Find the vertex of the graph of each quadratic function by completing the square or using the vertex formula. $$ f(x)=x^{2}+8 x+7 $$

Use the square root property to solve each equation. $$ x^{2}=16 $$

Graph each quadratic function. Label the vertex and sketch and label the axis of symmetry. \(f(x)=x^{2}-1\)

Use the quadratic formula to solve each equation. These equations have real number solutions only. $$ p^{2}+11 p-12=0 $$

Write the solution set in interval notation. $$ (x+1)(x+5) \leq 0 $$

Find the vertex of the graph of each quadratic function by completing the square or using the vertex formula. $$ f(x)=x^{2}+6 x+5 $$

Use the square root property to solve each equation. $$ x^{2}=49 $$

Graph each quadratic function. Label the vertex and sketch and label the axis of symmetry. \(h(x)=x^{2}+3\)

Use the quadratic formula to solve each equation. These equations have real number solutions only. $$ 2 y=5 y^{2}-3 $$

Write the solution set in interval notation. $$ (x-3)(x+4) \leq 0 $$

Solve. See Example 1. $$ x-2 \sqrt{x}=8 $$

Find the vertex of the graph of each quadratic function by completing the square or using the vertex formula. $$ f(x)=-x^{2}+10 x+5 $$

Use the square root property to solve each equation. $$ x^{2}-7=0 $$

Graph each quadratic function. Label the vertex and sketch and label the axis of symmetry. \(f(x)=(x-5)^{2}\)

Use the quadratic formula to solve each equation. These equations have real number solutions only. $$ 5 x^{2}-3=14 x $$

Write the solution set in interval notation. $$ (x+4)(x-1)>0 $$

Find the vertex of the graph of each quadratic function by completing the square or using the vertex formula. $$ f(x)=-x^{2}-8 x+2 $$

Use the square root property to solve each equation. $$ x^{2}-11=0 $$

Solve. See Example 1. $$ x-\sqrt{2 x}=4 $$

Graph each quadratic function. Label the vertex and sketch and label the axis of symmetry. \(g(x)=(x+5)^{2}\)

Use the quadratic formula to solve each equation. These equations have real number solutions only. $$ x^{2}-6 x+9=0 $$

Write the solution set in interval notation. $$ x^{2}+8 x+15 \geq 0 $$

Find the vertex of the graph of each quadratic function by completing the square or using the vertex formula. $$ f(x)=5 x^{2}-10 x+3 $$

Use the square root property to solve each equation. $$ x^{2}=18 $$

Solve. See Example 1. $$ \sqrt{9 x}=x+2 $$

Graph each quadratic function. Label the vertex and sketch and label the axis of symmetry. \(h(x)=x^{2}+5\)

Use the quadratic formula to solve each equation. These equations have real number solutions only. $$ y^{2}+10 y+25=0 $$

A projectile is fired straight up from the ground with an initial velocity of 80 feet per second. Its height \(s(t)\) in feet at any time \(t\) in seconds is given by the function \(s(t)=-16 t^{2}+80 t\). Find the interval of time for which the height of the projectile is greater than 96 feet.

Write the solution set in interval notation. $$ x^{2}-7 x+10 \leq 0 $$

Use the square root property to solve each equation. $$ y^{2}=20 $$

Graph each quadratic function. Label the vertex and sketch and label the axis of symmetry. \(h(x)=x^{2}-4\)

Use the quadratic formula to solve each equation. These equations have real number solutions only. $$ x^{2}+7 x+4=0 $$

Write the solution set in interval notation. $$ 3 x^{2}+16 x<-5 $$

Solve. See Example 2. $$ \frac{2}{x}+\frac{3}{x-1}=1 $$

Find the vertex of the graph of each quadratic function by completing the square or using the vertex formula. $$ f(x)=-x^{2}+x+1 $$

Use the square root property to solve each equation. $$ 3 z^{2}-30=0 $$

Graph each quadratic function. Label the vertex and sketch and label the axis of symmetry. \(h(x)=(x+2)^{2}\)

Use the quadratic formula to solve each equation. These equations have real number solutions only. $$ y^{2}+5 y+3=0 $$

Write the solution set in interval notation. $$ 2 x^{2}-5 x<7 $$

Find the vertex of the graph of each quadratic function by completing the square or using the vertex formula. $$ f(x)=x^{2}-9 x+8 $$

Use the square root property to solve each equation. $$ 2 x^{2}=4 $$

Graph each quadratic function. Label the vertex and sketch and label the axis of symmetry. \(H(x)=(x-1)^{2}\)

Use the quadratic formula to solve each equation. These equations have real number solutions only. $$ 8 m^{2}-2 m=7 $$

Write the solution set in interval notation. $$ (x-6)(x-4)(x-2)>0 $$

Solve. See Example 2. $$ \frac{3}{x}+\frac{4}{x+2}=2 $$

Use the square root property to solve each equation. $$ (x+5)^{2}=9 $$

Graph each quadratic function. Label the vertex and sketch and label the axis of symmetry. \(g(x)=x^{2}+7\)