Question

30 Use the method of completing the square to determine the vertex of f(x) = x² - 14x - 15.

State the coordinates of the vertex.

Answer 1

x² - 14x - 15 = (x − 7)² − 64

Then the coordinates of the vertex are (7 , -64)

Explanation:

x² - 14x - 15 = x² - 14x + (49 - 49) - 15

= (x² - 14x + 49) - 49 - 15

= (x² - 14x + 7²) - 49 - 15

= (x − 7)² − (49 + 15)

= (x − 7)² − 64

x² - 14x - 15 = (x − 7)² − 64

Then the coordinates of the vertex are (7 , -64)