Quadratic Translations

Question

How can I solve the question: Determine the vertex form equation of the parabola that is congruent (same shape) to the parent parabola (y=x2), has a vertex at (-3,-7) and is opening down.

Answer 1

vertex (-3,-7) is the maximum point for a downward opening parabola

y = a(x+3)^2 -7

if the parent parabola is y=x^2

the child parabola is translated down, vertically by 7

and horizontally by 3, to the right

Unless compressed or stretched a =-1. to be downward opening a<0

and it's

y= f(x) =- (x+3)^2 -7 in vertex form

f(x) = -(x-h)^2 + k where the vertex = (h,k)= (-3, -7)