Question

Determine the exact equation of the function given the info: 4th degree function touches the x-axis at -4, crosses x-axis at 0 and 2. (-1,54) is a point on function.

Answer 1

I got\[P(X)=-6x^2(x+4)(x-2)\]. Taht is incorrect.

Answer 2

a double root exists at x = -4 or (x+4)^2
roots at ( x) and ( x - 2)

so P(x) = (x)(x-2)(x+4)^2+C

let P(X) = 54 and substitute x = 1 into the right hand side and solve for C

Answer 3

Ok. Thank you very much, Soup Maker. You assistance is appreciated.