Question

Complete the square to determine the minimum or maximum value of the function defined by the expression. x2 − 10x + 15

Answer 1

• minimum: -10

Explanation:

Add and subtract the square of half the x-coefficient:

x² -10x +(-5)² -(-5)² +15

Express the first three terms as a square; simplify the remaining terms.

(x -5)² -10

This expression describes a parabola that opens upward and has its vertex at (x, y) = (5, -10). The minimum value is -10.