Vertex of a Function

[Drakkith]

Main Question or Discussion Point

I have the following function and I'm supposed to find the vertex of its graph.

f(x)=-3(x-2)²-3

Why is the vertex (2,-3) instead of (-2,-3)?

Edit: Bah, nevermind. I just realized the formula has (x-h) in it, not (x+h) in it...

 

[HallsofIvy]

Do you understand why the formula for vertex involves x- h, not x+ h?

The crucial point is that if x= 2, (x- 2) will be 0 so that f(2)= -3. If x is any other number (including -2) x- 2 will NOT be 0 so that, because the square of any non-zero number is positive, -3(x-2)^2 will be negative and f(x)= -3(x- 2)^2- 3 will be lower than three. (2, -3) is the highest point on the graph.