This week in Precalc 11 we learned how to solve an inequality algebraically with parabolas.

When you are given a graph that already has a parabola on it or you are given an equation, you are able to solve it using inequalities. If you are given a parabola that is opening up with the answer above zero, it will have two different answers. Before you are able to figure out the inequality you have to factor it first, by using what we learned in previous units.

If this is your equation:

you first have to factor it:

then, you solve for the x-intercepts:

and now you know that your parabola crosses through the x-axis at -10 and -1. Since the equation is above zero, you already know that there are going to be 2 separate inequalities that you are going to have. All of the numbers that are above zero are on the outside of the graph, so the inequalities would look like this:

Now if you have an equation that was less than zero:

you first have to factor it:

then, you solve for the x-intercepts:

and now you know that your parabola crosses through the x-axis at -5 and 5. Since the equation is below zero, you already know that there is going to be one inequality answer that you are going to have. All of the numbers that are below zero are in the middle part of the graph, so the inequalities would look like this: