Last week I talked about how to graph linear inequalities, so I think it’s fitting to talk about how to graph quadratic inequalities this time.

Like last time, the first thing we do is graph it as an equation.

Turn into standard form, we can treat it as a quadratic equation for now.

Now, to make this an inequality, we basically do the same thing as with linear equations.

Choose a point, and if the statement is true then that’s the side of the line that needs to be shaded. Concerning the line itself, the rules are also the same. Dotted line = not including.

0<(0-4)^2-6

0<16-6

0<10 is true

To add on a little more, we can write this in interval notation.

We start by factoring, but quickly looking at the original quadratic we can tell it’s not factorable, which isn’t that big of a deal as we have alternate methods such as using the quadratic formula.

Now we have the x-intercepts, and we can determine where the quadratic is above the x axis, since we need to know where the quadratic function is greater than y=0.

The parabola opens upwards in both directions to infinity, so the parabola is greater than y=0 in both of those directions.