Question

a parabola has vertex (-6,-12) AND PASSES THROUGH (6,24) find its equation in the form ax^2+bx+c

Answer 1

let the equation be in the form
y = a(x-h)^2 + k, where (h,k) is the vertex

so we have
y = a(x+6)^2 - 12
plug in the point (6,24) to get a
24 = a(12)^2 - 12
a = 36/144 = 1/4

so y = (1/4)(x-6)^2 - 12

expand this to change it into the required form

Please check my arithmetic, I am still on my first cup of coffee.