For the function f(x) = x2 + 4x - 12 solve the following.
f(x) < 0

(-6,2)

Step-by-step explanation:

We are given .

So we need to solve:

First let's find when the expression on the left is 0.

.

The expression on the left is factorable.

Given the coefficient of is 1, all we have to do is see if there are two numbers that multiply to be -12 and add to be 4.

Those numbers are 6 and -2 so the factored form is:

So the solutions can be found be solving the following linear equations:

and .

First equation, you just need to subtract 6 on both sides.

Second equation, you just need to add 2 on both sides.

So draw a number line with those on it and test the intervals they divide.

--------(-6)--------(2)----------

So we need to test three intervals.

*Plug in a number before -6 to see if that piece of the function is above the x-axis or below. We are looking for below since we want .

Let's plug in x=-8

or use .

so this piece is above since 20 is positive and not negative.

So we will not include this interval in our answer.

*Plug in a number between -6 and 2 like 0.

so this piece is under since -12 is negative and not positive.

So our solution includes the interval (-6,2).

*Plug in a number after 2 like 5.

so this piece is above since 33 is positive and not negative.

The answer only includes the interval (-6,2).

14

step-by-step explanation: