Chapter 7

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

Solve the given quadratic equations using the quadratic formula. If there are no real roots, state this as the answer. Exercises \(3-6\) are the same as Exercises \(13-16\) of Section 7.2. $$x^{2}+2 x-15=0$$

Solve the given quadratic equations by using the square root property. $$x^{2}=25$$

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. $$x(x-2)=4$$

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

Solve the given quadratic equations using the quadratic formula. If there are no real roots, state this as the answer. Exercises \(3-6\) are the same as Exercises \(13-16\) of Section 7.2. $$x^{2}-8 x-20=0$$

Solve the given quadratic equations by using the square root property. $$x^{2}=100$$

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. $$(3 x-2)^{2}=2$$

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. If there are no real roots, state this as the answer. Exercises \(3-6\) are the same as Exercises \(13-16\) of Section 7.2. $$D^{2}+3 D+2=0$$

Solve the given quadratic equations by using the square root property. $$x^{2}=7$$

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. $$x^{2}=(x+2)^{2}$$

Solve the given quadratic equations using the quadratic formula. If there are no real roots, state this as the answer. Exercises \(3-6\) are the same as Exercises \(13-16\) of Section 7.2. $$t^{2}+5 t-6=0$$

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 by using the square root property. $$s^{2}=15$$

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. $$x\left(2 x^{2}+5\right)=7+2 x^{2}$$

Solve the given quadratic equations using the quadratic formula. If there are no real roots, state this as the answer. Exercises \(3-6\) are the same as Exercises \(13-16\) of Section 7.2. $$x^{2}-5 x+3=0$$

Solve the given quadratic equations by using the square root property. $$2 y^{2}-5=1$$

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 using the quadratic formula. If there are no real roots, state this as the answer. Exercises \(3-6\) are the same as Exercises \(13-16\) of Section 7.2. $$x^{2}+10 x-4=0$$

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 by using the square root property. $$4 x^{2}-7=2$$

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. If there are no real roots, state this as the answer. Exercises \(3-6\) are the same as Exercises \(13-16\) of Section 7.2. $$v^{2}=15-2 v$$

Solve the given quadratic equations by using the square root property. $$(x-2)^{2}=25$$

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. $$y^{2}(y-2)=3(y-2)$$

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

Solve the given quadratic equations using the quadratic formula. If there are no real roots, state this as the answer. Exercises \(3-6\) are the same as Exercises \(13-16\) of Section 7.2. $$16 V-24=2 V^{2}$$

Solve the given quadratic equations by using the square root property. $$(x+2)^{2}=10$$

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. $$z(z+4)=(z+1)(z+5)$$

Solve the given quadratic equations using the quadratic formula. If there are no real roots, state this as the answer. Exercises \(3-6\) are the same as Exercises \(13-16\) of Section 7.2. $$8 s^{2}+20 s=12$$

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 by factoring. $$x^{2}-25=0$$

Solve the given quadratic equations by using the square root property. $$(y+3)^{2}=7$$

Solve the given quadratic equations using the quadratic formula. If there are no real roots, state this as the answer. Exercises \(3-6\) are the same as Exercises \(13-16\) of Section 7.2. $$4 x^{2}+x=3$$

Sketch the graph of each parabola by using the vertex, the \(y\) -intercept, and the \(x\) -intercepts. Check the graph using a calculator. $$u=-3 v^{2}+12 v-9$$

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

Solve the given quadratic equations by using the square root property. $$\left(x-\frac{5}{2}\right)^{2}=100$$

Solve the given quadratic equations using the quadratic formula. If there are no real roots, state this as the answer. Exercises \(3-6\) are the same as Exercises \(13-16\) of Section 7.2. $$3 y^{2}=3 y+2$$

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 by factoring. $$4 y^{2}=9$$

Solve the given quadratic equations by completing the square. $$x^{2}+2 x-15=0$$

Solve the given quadratic equations using the quadratic formula. If there are no real roots, state this as the answer. Exercises \(3-6\) are the same as Exercises \(13-16\) of Section 7.2. $$3 x^{2}=3-4 x$$

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. $$s=t^{2}+2 t+2$$

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

Solve the given quadratic equations by completing the square. $$x^{2}-8 x-20=0$$

Solve the given quadratic equations using the quadratic formula. If there are no real roots, state this as the answer. Exercises \(3-6\) are the same as Exercises \(13-16\) of Section 7.2. $$z+2=2 z^{2}$$

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. $$y=-2 x^{2}-2 x-6$$

Solve the given quadratic equations by factoring. $$x^{2}-5 x-14=0$$