Solve Quadratic Equations Algebraically - Example 1
Solve Quadratic Equationsby Factoring - Example 1
Solve Quadratic Equationsby Graphing - Example 1
Solving Quadratic Equationsby Completingthe Square - Example 1
The Discriminant - Example 1
Liberty University
Graph Quadratic Inequalities - Example 1


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equation. Why is less than negative? Two. X Square plus three x plus five Star. This is an inequality nine equation. Before we graph it, let's go ahead. We're gonna make an X y table and we can find a couple of points and kind of go from there because, remember, we're gonna try to pick about five points. So let's go ahead and let's. First of all, let's find our y intercept or why intercepts we confined with our constants, or constant is five. So that means when x zero why is going to be five so we can go ahead and graph that one point on a graph. The other thing we confined is our axes of symmetry. Axis of symmetry is negative. Be over to a So that would be negative. Three over two times Negative too. So that's gonna be negative. Three over negative four or positive, 3/4. So that's gonna be kind of in between a with one and the zero. But it's gonna be a little bit closer to the one. Okay, so we're not gonna find that point, but we're going to kind of use it. We can kind of see So let's pick some points to the left and to the right. But we've already got zero on the left of it. So let's go ahead and do one. So if I put that in wise less than negative two times one squared plus three times one plus five, that's gonna mean that wise less than negative two plus three plus five or one plus five. So that means that wives less than six. So for one, we're gonna have six. Then let's go ahead and less find. Well, let's just go backwards. Let's go. Negative one. So if I put negative one in place, what I'm going to get is I'm going to get zero. I'm gonna come and save us some time and do a few them this way. So that's gonna be right here. And then let's go ahead and let's pick. Let's be positive, too. So if I put positive to again, I'm going to get three for right there. So my points aren't completely even. That's okay. We can still see the shape of the parabola. So, um, I think that kind of gives us enough to kind of decide where parable is. If we want to do another one. If you wanted to do three, you could do three. So you could have negative too. Um, which would be negative four. So we kind of have some in between spots on this one. So I think we've got enough. We can go ahead and graph. So this is going to be it does not say greater than or equal. It doesn't say equal to So this is gonna be a dotted line, and so we're going to kind of just draw it out with a dotted line. I'm kind of extended since it extends on both sides and it says that it is less sense. So that means we're gonna be shading now when you're talking about parabola, if it's less than you may have to shade inside the actual parable. And in this case, that's exactly what we're gonna dio. We're gonna shade on the inside of our parappa and it would stay in between. However those lines go, it would stay in between those lines

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