What is the equation of the parabola with a vertex at (-4,5), that opens up, and is congruent to the quadratic function y=-1/4x^2

y = - 1/4 (x+4) ² + 5

Step-by-step explanation:

A parabola which is congruent to y = - 1/4x² must have the same stretch factor.

The stretch factor is - 1/4.

Since we are given the vertex, use the equation for a quadratic function in vertex form: y = a (x-h) ² + k

The vertex is (h, k). Whatever h seems to be in the equation, it is actually the negative because vertex form uses its negative.

Substitute the vertex and the stretch factor into the equation.

The stretch factor is represented by the variable "a".

"h" will be 4 because its the opposite sign than the actual vertex,

"k" will be 5 because it remains the same sign.

y = - 1/4 (x+4) ² + 5