Question

What is the maximum value that the graph of `-3x^2 - 12x + 15`?

Answer 1

See explanation.

Explanation:

This is a quadratic function with a negative coefficient of `x^2`, so it reaches its maximum value at the vertex of the parabola.

Its coordinates can be calculated as:

`p=-b/(2a)`

and

`q=-Delta/(4a)`

but you can also calculate `q` by substituting `p` to the function's formula:

`p=12/(-6)=-2`

`q=f(-2)=-3*(-2)^2-12*(-2)+15`

`q=-3*4+12*2+15=-12+24+15=27`

Answer:

The maximum value is `27` at `x=-2`

This can be checked by looking at the graph:

graph{-3x^2-12x+15 [-10, 10, -40, 40]}