This week in Precalculas 11 we went over inequalities and what they mean. We also learned how to graph them. In graphing inequalities, we can use what ve learned from the last unit, like vertex, x-intercept, y-intercept, etc. to help us graph inequalities.

Example : y> – (x+4)^2

• first I graphed the expression on demos without the inequality sign to see what it would look like. in this example we already have the inequality in vertex form so it is easy to graph but if we dont have to solve it a little bit.

• now that I plugged in the inequality sign there are some changes we can see so let’s break it down

1. As you can see the parabola has a dashed line, this is because our inequality does not have the small line under it. This means that y is greater than… If it was greater than or equal we would but a bold line.
2. Everything outside the graph is shaded. This is because of the inequality sign. Our expression is telling us that our solution has to be greater than – (x+4)^2. So how to we figure out where to shade.

• take a random point in a graph and plug in the x and y into the original function
• if you get a true statement then this means that the shading should go in this zone. In this case it is outside the parabola.