Here we have three coordinate pairs and we're looking for the parable A that would contain all three pairs. So the equation for a parabola could take the form. Why is equal toe a X squared plus B X plus C, where A B and C are constants? And we confined those because of our three port repairs? We could make three equations and we'll have those three unknowns and we'll be ableto find are coefficients. So our first a question equation is a times X squared. In this case, negative one is our ex plus B times negative one plus c equals why, in this case, negative five. Our second equation we're going to use to for the X two x squared plus B times two plus c equals why which here is seven and our third equation. The X is five. So eight times five squared plus B times five plus c equals why, which is one. And we can clean these up a little bit. Negative one squared is one. So we have a minus. B plus C equals negative five on our second equation to swear this four. So for a plus to be plus C equals seven on our third equation five squared this 25 25 a plus five B plus C equals one. Now all three equations The sea has a coefficient of one. So we're gonna eliminate those first. That will be pretty straightforward. So it's called the top equation E one and our next equation e to on our 3rd 1 e three and we'll go ahead and take e one and multiply it by negative one. So we will have a negative A plus B minus C equals positive five and we'll take E to as is so that will be for a plus to the plus C equals positive. Seven. Negative and positive for a leaves us three a one plus to his threes. We have three be the seas got eliminated and five plus seven ist 12. We could divide every single term by three and we get a plus. B equals for now. Let's do the same thing over here using e three instead of e too. So well again, we'll take negative e one, which was negative. A positive be negative. C equals positive five. And when we add these two together 25 minus one is 24 so you get 24. A five plus one is six. So we get six. Be the Caesar eliminated and one plus five of six. If we divide every single term by six, we get that for a plus. Be equals one. And now, if we let's call this equation that we got to below a plus B equals for we'll call that a four and, well, take that and will multiply it by negative one so negative e for well, give us negative. A minus bi equals negative or so four minus one is 33 a. The bees eliminated equals negative three. And if we divide both sides by three, we get a is equal to negative one. So there's our first. Now it could come back over to eat for and say will be equals for minus a, which equals four minus negative one, which equals positive. Five. So B equals five. It's our second, and then we'll use a minus. B plus C will use this equation. You want to determine C so a is negative. One minus B. So minus five plus C equals negative five. So negative one and negative five is negative. Six. If we add six to both sides, we get that C equals positive one. So our solution set is negative. One five positive one. And that's that What we were asked to find. And if you actually wanted to know the equation for the proble, you would say that why equals negative X squared plus five x plus one. In fact, for fun. If you graphed that using a graphing utility and you plot all three points, you'll see that, indeed, they lie on the graph.