Question

Determine and state the vertex of f(x) = x2 - 2x - 8 using the method of completing the square

Answer 1

vertex = (1, - 9 )

Explanation:

The equation of a parabola in vertex form is

f(x) = a(x - h)² + k

where (h, k) are the coordinates of the vertex and a is a multiplier

Given

f(x) = x² - 2x - 8

To complete the square

add/ subtract ( half the coefficient of the x- term )² to x² - 2x

f(x) = x² + 2(- 1)x + 1 - 1 - 8

= (x - 1)² - 9 ← in vertex form

with vertex = (1, - 9 )