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.

see explanation

Step-by-step 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

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b

2

−

b

b

3

+

7

b

2

+

14

b

+

6

%

−

3

b

3

+

7

b

2

+

14

b

+

6

%

step-by-step explanation: