What is the minimum value of the function g(x) = x^2 - 6x - 12?

9514 1404 393

  -21

Step-by-step explanation:

I find it convenient to read the value from the graph created by a graphing calculator. The minimum is -21.

__

The function can be rearranged to vertex form, which also shows the minimum value.

  g(x) = (x^2 -6x +9) -12 -9*

  g(x) = (x -3)^2 -21 . . . . . . . . vertex form

The vertex is (3, -21), so the minimum is -21.

_____

* we added the square of half the x-coefficient inside parentheses, and its opposite outside parentheses. This makes the expression inside parentheses a perfect square trinomial.

the ratio of grapes to blueberries she should use is 12: 3

step-by-step explanation:

if mandie is making 15 cups of fruit salad, the ratio of grapes to blueberries she should use is 12: 3.

irrational, cannot