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

minimum: - 10

Step-by-step 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.