Question

Complete the square to rewrite y= x2 - 6x + 2 in vertex form. Then state

whether the vertex is a maximum or a minimum and give its coordinates.

Answer 1

The vertex is a minimum.

Answer 2

see explanation

Explanation:

Given

y = x² - 6x + 2

The equation of a parabola in vertex form is

y = a(x - h)² + k

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

To complete the square

add/subtract ( half the coefficient of the x- term )² to x² - 6x

y = x² + 2(- 3)x + 9 - 9 + 2

= (x - 3)² - 7 ← in vertex form

with vertex = (3, - 7 ) and a = 1

Since a > 0 then vertex is a minimum