Cubic

  1. degree: odd
    coefficient: positive

  2. 3 x intercepts

  3. 2 direction changes
    +1=3

  4. The minimum degree is 3

  5. x-intercepts: -1, 2, 3
    Written as factors: (x+1)(x-2)(x-3)

  6. f(x)=a(x+1)(x-2)(x-3)

  7. Plug in the point (0,12) and solve for a
    12=a(0+1)(0-2)(0-3)
    12=a(1)(-2)(-3)
    12=6a
    a=2

  8. The function of this graph is
    f(x)=2(x+1)(x-2)(x-3)
    or
    f(x)=2x^3-8x^2+2x+12