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