Question

Find the minimum or maximum value off
x^2 + 6x +11

Answer 1

The minimum is the point (-3,2)

Explanation:

we have

`x^(2) +6x+11`

This is a vertical parabola open upward (because the leading coefficient is positive)

The vertex is a minimum

Convert the equation in vertex form

Complete the square

`f(x)=(x^(2) +6x+3^2)+11-3^2`

`f(x)=(x^(2) +6x+9)+11-9`

`f(x)=(x^(2) +6x+9)+2`

Rewrite as perfect squares

`f(x)=(x+3)^(2)+2` ----> equation in vertex form

The vertex is the point (-3,2)

therefore

The minimum is the point (-3,2)