y = x ^ (2) - 6x + 2 rewrite in vertex form and state whether its maximum or 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

To obtain this form use the method of completing 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)

To determine whether maximum or minimum consider the value of a

• If a > 0 then minimum

• If a < 0 then maximum

here a = 1 > 0 ⇒ minimum

Hence (3, - 7) is a minimum