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