Question

Complete the square to rewrite y = x2 - 6x + 3 in vertex form. Then state

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

Answer 1

see explanation

Explanation:

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

Given

y = x² - 6x + 3

To complete the square

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

y = x² + 2(- 3)x + 9 - 9 + 3

= (x - 3)² - 6 ← in vertex form

• If a > 0 then vertex is a minimum

• If a < 0 then vertex is a maximum

Here a = 1 > 0, thus

(3, - 6 ) is a minimum