Question

Complete the square to rewrite y = x2 - 6x + 16 in vertex form. Then state

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

Answer 1

minimum (3,7)

Explanation:

y = x^2 - 6x + 16

Take the coefficient of the x term -6

Divide it by 2 -6/2 =-3

Then square it ( -3)^2 =9

Add that to the equation (remember if we add it we must subtract it)

y = x^2 - 6x +9 -9+ 16

y = (x^2 - 6x +9) -9+ 16

The term inside the parentheses is x+b/2 which is x+ -3 or x-3 quantity squared

y = (x-3)^2 +7

This is in vertex form

y = a(x-h)^2 +k where (h,k) is the vertex

(3,7) is the vertex

Since a=1, it is positive, so it opens upward and the vertex is a minimum