# Problem Set 4

1. Inequalities. a) x<3 b) -2<x<3 c) -\frac{5}{3}<x<\frac{5}{3} d) -\frac{5}{3}<x<-1\vee 1<x<\frac{5}{3}
2. Looking at the Vertex 1. a) (1.5,-20.25) b) (-3,0);(6,0) c) (1.5,0) d) x=1.5
3. Looking at the Vertex 2.

If the x-intercepts are the same, then the vertex and x-intercept are the same point.

The x-coordinate of the vertex is the same as the x-coordinate of the midpoint of the x-intercepts.

The vertical line through the vertex passes through the midpoint of the x-intercepts

4. Investigating the Solutions 1.

d _________ d

c ____________ c

__________ b

________ a

5. Investigating the Solutions 2.

x-intercept (-\frac{5}{2}-\frac{\sqrt{65}}{2},0)

x-intercept (-\frac{5}{2}+\frac{\sqrt{65}}{2},0)

y-intercept (0,-10)

vertex (-\frac{5}{2},-\frac{65}{4})

6. Investigating the Solutions 3.

vertex and x-intercept (3,0)

y-intercept (0,-9)

7. Investigating the Solutions 4.

y-intercept (0,10)

vertex (3,1)

8. Investigating the Solutions 5.

A

C

B

9. Quadratic Equations. a) 1\pm 2\sqrt{3} b) \frac{5}{2}\pm \frac{\sqrt{65}}{2} c) none d) -\frac{5}{6}\pm \frac{\sqrt{145}}{6}
10. Transforming Parabolas.

0 1 0 0

0 0 0 5

2 0 0 0

0 6 3 0