I need to find a polynomial f. such that f(4)=0 f(-3)=0 and f(0)=8 that models the speed of a roller coaster.

Question

I have no Idea how to start and my teacher said figure it out.

Answer 1

You were given 2 zeros of a polynomial, so start with

f(x) = A(x - 4)(x + 3),

where A is real and A ≠ 0. Find A knowing that f(0)=8.

A(0 - 4)(0 + 3) = 8

-12A = 8

A = -8/12 = -2/3

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