The Vertex of a Parabola
Given a function of the form:

Its graph has a shape known as a parabola. The vertex of a parabola is the point of its maximum or minimum value.
The x-coordinate of the vertex is given by:

Given the function:

It's evident that a =1, but we don't have b or c.
Calculating xv:

We are given this value is -5, thus:

Substitute the value of b in the function:

We are also given the value of y = 6 when x=-5. Substituting:

Operating:

The required coefficients are b = 10 and c = 31