Find b and c of the equation

Question

Find b and c so that y=-12x^2 +bx+c has the vertex (5,-5)

Answer 1

You could start by putting the quadratic in vertex form

y=a(x-h)²-k where (h,k) is the vertex

y=a(x-5)²-5

y=a(x-5)(x-5)-5

y=a(x²-10x+25)-5

Distribute the a

y=ax²-10ax+25a-5

We know that ax² = -12x² so a=-12

b will equal -10a so b=-10(-12)=120

c equals 25a-5 so c=25(-12)-5=-305