Verified answer

y = 10x^2 + bx + c

first, work with y'

y' = 20x + b

as the vertex is (-8;-9) which we southerners call the turning point, then y' = 0 where x = -8

so 0 = 20(-8) + b

0 = -160 + b

b = 160

now just work out c

y = 10x^2 + 160x + c

sub (-8;-9)

-9 = 10(64) + 160(-8) +c

-9 = 640 - 1280 + c

631 = c

y = 10x^2 + 160x + 631