Find b and c so that y=2x^2+bx+c has vertex (-5,-5)

Answer 1

the vertex tells us that
y = a(x+5)^2 - 5
so
ax^2 + 10ax + 25a-5 = 2x^2 + bx + c
a=2
b = 10a = 20
c = 25a-5 = 45
check:
2x^2 + 20x + 45 = 2(x+5)^2 - 5