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Liberty University
Graph Quadratic Inequalities - Example 3


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squared minus six. Why is less than X squared minus 16? So we're going to create an X Y table, and we're gonna go ahead and find a few points to help us do this. One first thing we're gonna find is we're gonna find our y intercept now. Why? Intercepts is based on our constant, which in this case is negative. 16. So we're X zero. Why, It's gonna be negative. 16. Now, I'm not gonna graph on this graph, but you could if you needed Thio. So now let's also find the axis of symmetry. The axis of symmetry says it's negative. Be over to a well, in this case are be a zero and times two times one which is still gonna be 0/2, which is zero. So our axes of symmetry is actually going to be on the Y axis, so that will allow us to kind of decide where we want to go from there. So let's pick a couple of points and let's just kind of go for the left and right, and to kind of give us some room. Why don't Because of that, we can tell that the Vertex is gonna because we know the Y intercept. It's negative. 16. So it's gonna be kind of coming down pretty low. So let's skip over. Let's do negative two. And positive too. We'll do those first. So that means we're gonna have why is less than two squared minus 16, which is four minus 16, which is going to be negative. 12. Why is less than negative? Two squared minus 16 is also gonna be four minus 16. So that was also gonna be negative. 12. Yeah, my graphs. Not quite that small, solicitous move on and let's do three and negative three. Well, if I plug those in, a three is going to give me a negative seven. Negative three is also going to give me negative seven. So those will be those points. Um, let's keep going. Let's do four and negative four. So that would be four squared would be 16 minus 16 would be zero in both these cases, and we can kind of see it's going to kind of go below. I know this is gonna This equation is positive, so that means it's gonna have a minimum value now. It's also a, um it doesn't say greater than er equal to. So it's gonna be a dotted line. So I'm gonna go ahead and draw the deadline, but this one is not gonna be. It's gonna be kind of cut off the graph, so I'm not gonna have the Vertex on the graph. So I'm just going to kind of let it go to the bottom and stop and then just bring it back up Now we also can look at where we need to shade. This one says less than so. That means we need to shade below the graph. So that means we're gonna shade this area right here. It obviously we can't get exactly below the graph because our graph is going to fall off. The actual parable is not only full graph the bottom of it, but we can show the area to show and demonstrate