Write the equation of the quadratic function with roots -10 and -8 and a vertex at (-9, -3).

Roots at x=-10 and x=-8

if a function has roots at x=r1 and x=r2, then the factored form is
f(x)=a(x-r1)(x-r2) where a is a constant
so

roots -10 and -8
f(x)=a(x-(-10))(x-(-8))
f(x)=a(x+10)(x+8)
now
use (-9,-3)
-3=a(-9+10)(-9+8)
-3=a(1)(-1)
-3=-a
3=a

the equation is
y=3(x+10)(x+8)
or expanded
y=3x²+54x+240