This week in Pre calculus we learned about solving quadratic inequalities.

Solving quadratic inequalities is quite similar to solving quadratic equalities, but there are a few additional things that must be considered.

When solving quadratic inequalities, you must always keep in mind, that if you flip the positive/negatives of the inequality, you must also flip the sign, so if the sign is “less than”, you must flip it to “greater than”.

example:

0 < – x² + 6x + 9

First, we can flip the negative sign, and make it positive. But remember: when we do this, we must also flip the inequation symbol.

Which will look like this:

0 > x² + 6x + 9

Now, we can factor the inequation:

0 > (x + 3)²

Now, we must do the restrictions. We know that X cannot equal -3, because 0 is not greater than 0.