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.

see explanation

Step-by-step 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