Parabolas and Completing the Square
(Angelo State University)
If y = -x² + 4x – 10, find the largest value attained by y. Do this without using calculus.

The solution to the problem is to find the vertex for the parabola. One approach is to complete the square and obtain

So the graph is a parabola opening down, and the vertex is at the point (x, y) = (2, -6).

Hence the largest value is y = -6.