#1

  1. degree: even
    coefficient: positive

  2. 3 x intercepts

  3. 3 direction changes
    +1=4

  4. Degree is at least 4

  5. x-intercepts are: -1, 5
    The graph is tangent to the x axis at 1 so (x-1)^2 is a factor
    Written as factors: (x+1)(x-1)^2(x-5)

  6. f(x)=a(x+1)(x-1)^2(x-5)

  7. Plug in the point (0,-10) and solve for a-10=a(0+1)(0-1)(0-1)(0-5)
    -10=a(1)(-1)(-1)(-5)
    -10=a(-5)
    a=2

  8. The function of this graph is
    f(x)=2(x+1)(x-1)^2(x-5)
    or
    f(x)=2x^4-12x^3+8x^2+12x-10