Construct polynomial function

Question

Construct polynomial function y=f(x) with the following properties. Give the equation of the function in factored form:

-The graph of f rises on the left and falls on the right

-f has 3 zeros: x=-4, x=0, and x=3

-The multiplicity of x=3 is 2

Answer 1

f(x) = -(x-3)^2(x+4)x= the equation in factored form

(x^2-6x+9)(x^2+4x) =

f(x) = x^4-2x^3-15x^2+36x

just change the sign of any root and add it to x, then multiply them all together

but this rises on the right and falls on the left, to reverse it, just stick a negative sign in front

f(x) =-(x-3)^2(x+4)(x)