find a polynomial function such that f(x) is a second-degree function with zeros at x=3 and x=6 and f(-8) = -7

Question

find a polynomial function such that f(x) is a second-degree function with zeros at x=3 and x=6 and f(-8) = -7

please help.

I was trying to solve it like system of equations but with 3, but I keep getting different answers.

Answer 1

f(x) = a(x-3)(x-6)

f(-8) = -7 = a(-11)(-14)

a = -7/(11)14) = -1/22

f(x) = (-1/22)(x-3)(x-6)

f(x) = -x^2/22 + 9x/22 -18/22

check the answer

f(-8) = -7 = -(-8)^2/22 + 9(-8)/22 -9/11

= -64/22- 72/22 -18/22

=(-64-72-18)/22= -154/22=-7