Question

x=-10 and x=-8 and a vertex at (-9, -3).
Leave your answer in the form:
f(x)=(a)(x^2+bx+c)

Answer 1

i am going to assume that the first two are the zeros start with
\[f(x)=a(x+10)(x+8)\] and then find \(a\) using the vertex

Answer 2

alternatively you could write \(f(x)=a(x+9)^2-3\) and solve for \(a\) using either zero

Answer 3

lets do the first method
\[f(x)=a(x+10)(x+8)\]
\[f(-9)=-3=a(-9+10)(-9+8)=a\times 1\times -1\] so we know
\[-a=-3\] and therefore \(a=3\) and you get
\[f(x)=3(x+10)(x+8)\]