Find the co-ordinates of the vertex and state whether it has a maximum or a minimum.?

Question

-3(x + 2)(x – 5)

Find the co-ordinates of the vertex and state whether it has a maximum or a minimum.

Answer 1

I assume this is equal to y?

If it is, it's definitely a maximum because it's a parabola that opens downward

Now I'll work on the vertex

Answer 2

First rewrite the equation:

-3x² + 9x + 30

Then differentiate and set equal to zero:

-6x + 9 = 0

6x = 9

x = 3/2

The vertex is (1.5, 36.75). If you graph x = 0 (0, 30) and x = 3 (3, 30), you'll find that it is a maximum.