# How do you find the max or minimum of #f(x)=-7-3x^2+12x#?

##### 2 Answers

Please see the explanation.

#### Explanation:

Because this question is in precalculus, I am going to assume that you have not, yet, studied differential calculus. Therefore, I am going to show you how to find the minimum or maximum of a quadratic by finding the vertex:

Let's begin by writing the quadratic equation in standard form:

The vertex form of the equation of a quadratic is:

where

Because "a" in -3, we shall add 0 to the original equation in the form

This allows us to factor a -3 from the first 3 terms:

Set the middle term of the right side of the pattern

Solve for h:

Substitute

Substitute 2 for every h:

Combine the constant terms:

We can see that the vertex is at

The maximum value that this quadratic achieves is 5, at the x coordinate 2.

Max of

#### Explanation:

First Derivative of

Second deivative of

At the turning point

Therefore

At the point

Therefore , the maximum value is 5