Question

Find the minimum or maximum of g(x)+x^2+9x-36. Explain how you know whether it is the minimum or the maximum.

Answer 1

It is a minimum because the parabola opens up. We know it opens up because it is 1x^2 and 1 is positive.

Answer 2

To find the minimum, put it in vertex form which is h,k form. Do this by completing the square:
I will demonstrate:

Answer 3

Now take 1/2 of the coefficient of x which is 9. Square that number and add it to the expression and then subtract it so as not to change the expression: