Chapter 7

Sketch the graph of each parabola by using only the vertex and the \(y\) -intercept. Check the graph using a calculator. \(y=x^{2}-6 x+5\)

Determine whether or not the given equations are quadratic. If the resulting form is quadratic, identify \(a, b,\) and \(c,\) with \(a>0 .\) Otherwise, explain why the resulting form is not quadratic. $$x(x-2)=4$$

Solve the given quadratic equations by finding appropriate square roots as in Example \(I\) $$x^{2}=25$$

Sketch the graph of each parabola by using only the vertex and the \(y\) -intercept. Check the graph using a calculator. \(y=-x^{2}-4 x-3\)

Determine whether or not the given equations are quadratic. If the resulting form is quadratic, identify \(a, b,\) and \(c,\) with \(a>0 .\) Otherwise, explain why the resulting form is not quadratic. $$(3 x-2)^{2}=2$$

Solve the given quadratic equations by finding appropriate square roots as in Example \(I\) $$x^{2}=100$$

Sketch the graph of each parabola by using only the vertex and the \(y\) -intercept. Check the graph using a calculator. \(y=-3 x^{2}+10 x-4\)

solve the given quadratic equations, using the quadratic formula. Exercises \(5-8\) are the same as Exercises \(11-14\) of Section 7.2. $$x^{2}+2 x-8=0$$

Solve the given quadratic equations by finding appropriate square roots as in Example 1. $$x^{2}=7$$

Determine whether or not the given equations are quadratic. If the resulting form is quadratic, identify \(a, b,\) and \(c,\) with \(a>0 .\) Otherwise, explain why the resulting form is not quadratic. $$x^{2}=(x+2)^{2}$$

Sketch the graph of each parabola by using only the vertex and the \(y\) -intercept. Check the graph using a calculator. \(s=2 t^{2}+8 t-5\)

solve the given quadratic equations, using the quadratic formula. Exercises \(5-8\) are the same as Exercises \(11-14\) of Section 7.2. $$x^{2}-8 x-20=0$$

Solve the given quadratic equations by finding appropriate square roots as in Example 1. $$s^{2}=15$$

Determine whether or not the given equations are quadratic. If the resulting form is quadratic, identify \(a, b,\) and \(c,\) with \(a>0 .\) Otherwise, explain why the resulting form is not quadratic. $$x\left(2 x^{2}+5\right)=7+2 x^{2}$$

Sketch the graph of each parabola by using only the vertex and the \(y\) -intercept. Check the graph using a calculator. \(R=v^{2}-4 v\)

solve the given quadratic equations, using the quadratic formula. Exercises \(5-8\) are the same as Exercises \(11-14\) of Section 7.2. $$D^{2}+3 D+2=0$$

Determine whether or not the given equations are quadratic. If the resulting form is quadratic, identify \(a, b,\) and \(c,\) with \(a>0 .\) Otherwise, explain why the resulting form is not quadratic. $$n\left(n^{2}+n-1\right)=n^{3}$$

Solve the given quadratic equations by finding appropriate square roots as in Example \(I\) $$(x-2)^{2}=25$$

Sketch the graph of each parabola by using only the vertex and the \(y\) -intercept. Check the graph using a calculator. \(y=-2 x^{2}-5 x\)

solve the given quadratic equations, using the quadratic formula. Exercises \(5-8\) are the same as Exercises \(11-14\) of Section 7.2. $$t^{2}+5 t-6=0$$

Solve the given quadratic equations by finding appropriate square roots as in Example 1. $$(x+2)^{2}=10$$

Determine whether or not the given equations are quadratic. If the resulting form is quadratic, identify \(a, b,\) and \(c,\) with \(a>0 .\) Otherwise, explain why the resulting form is not quadratic. $$(T-7)^{2}=(2 T+3)^{2}$$

Sketch the graph of each parabola by using the vertex, the \(y\) -intercept, and the \(x\) -intercepts. Check the graph using \(a\) calculator. \(y=x^{2}-4\)

solve the given quadratic equations, using the quadratic formula. Exercises \(5-8\) are the same as Exercises \(11-14\) of Section 7.2. $$x^{2}-4 x+2=0$$

Solve the given quadratic equations by finding appropriate square roots as in Example 1. $$(y+3)^{2}=7$$

$$\text { Solve the given quadratic equations by factoring.}$$ $$x^{2}-4=0$$

Solve the given quadratic equations by factoring. $$x^{2}-4=0$$

Sketch the graph of each parabola by using the vertex, the \(y\) -intercept, and the \(x\) -intercepts. Check the graph using \(a\) calculator. \(y=x^{2}+3 x\)

solve the given quadratic equations, using the quadratic formula. Exercises \(5-8\) are the same as Exercises \(11-14\) of Section 7.2. $$x^{2}+10 x-4=0$$

Solve the given quadratic equations by finding appropriate square roots as in Example 1. $$\left(x-\frac{5}{2}\right)^{2}=100$$

$$\text { Solve the given quadratic equations by factoring.}$$ $$B^{2}-400=0$$

Solve the given quadratic equations by factoring. $$B^{2}-400=0$$

Sketch the graph of each parabola by using the vertex, the \(y\) -intercept, and the \(x\) -intercepts. Check the graph using \(a\) calculator. \(y=-2 x^{2}-6 x+8\)

solve the given quadratic equations, using the quadratic formula. Exercises \(5-8\) are the same as Exercises \(11-14\) of Section 7.2. $$v^{2}=15-2 v$$

In Exercises \(11-30,\) solve the given quadratic equations by completing the square. Exercises \(11-14\) and \(17-20\) may be checked by factoring. $$x^{2}+2 x-8=0$$

$$\text { Solve the given quadratic equations by factoring.}$$ $$4 y^{2}=9$$

Solve the given quadratic equations by factoring. $$4 y^{2}=9$$

Solve the given quadratic equations by completing the square. Exercises \(11-14\) and \(17-20\) may be checked by factoring. $$x^{2}+2 x-8=0$$

Sketch the graph of each parabola by using the vertex, the \(y\) -intercept, and the \(x\) -intercepts. Check the graph using \(a\) calculator. \(y=-2 x^{2}-6 x+8\)

solve the given quadratic equations, using the quadratic formula. Exercises \(5-8\) are the same as Exercises \(11-14\) of Section 7.2. $$16 V-24=2 V^{2}$$

In Exercises \(11-30,\) solve the given quadratic equations by completing the square. Exercises \(11-14\) and \(17-20\) may be checked by factoring. $$x^{2}-8 x-20=0$$

$$\text { Solve the given quadratic equations by factoring.}$$ $$2 x^{2}=0.32$$

Solve the given quadratic equations by factoring. $$2 x^{2}=0.32$$

Solve the given quadratic equations by completing the square. Exercises \(11-14\) and \(17-20\) may be checked by factoring. $$x^{2}-8 x-20=0$$

Sketch the graph of each parabola by using the vertex, the \(y\) -intercept, and two other points, not including the \(x\) -intercepts. Check the graph using a calculator. \(y=2 x^{2}+3\)

solve the given quadratic equations, using the quadratic formula. Exercises \(5-8\) are the same as Exercises \(11-14\) of Section 7.2. $$8 s^{2}+20 s=12$$

In Exercises \(11-30,\) solve the given quadratic equations by completing the square. Exercises \(11-14\) and \(17-20\) may be checked by factoring. $$D^{2}+3 D+2=0$$

$$\text { Solve the given quadratic equations by factoring.}$$ $$x^{2}-8 x-9=0$$

Solve the given quadratic equations by factoring. $$x^{2}-8 x-9=0$$

Solve the given quadratic equations by completing the square. Exercises \(11-14\) and \(17-20\) may be checked by factoring. $$D^{2}+3 D+2=0$$