How to Graph a Parabola That Ends

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Graphing a parabola that ends is something that you can do in just a few quick moments of your time. Learn how to graph a parabola that ends with help from a mathematics tutor and educator in this free video clip.

Part of the Video Series: Graphing in Math
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Video Transcript

Hi there, this is Ryan Malloy here at the Worldwide Center of Mathematics. In this video we're going to discuss how to discuss a parabola that ends. Now typically when you're graphing a parabola, for example, let's say we're given Y equals 3X squared minus 5. Typically if you're asked to graph this it is usually assumed that this will be defined on all real numbers. It is said the domain is the set of all real numbers or sometimes written negative infinity to infinity and so if there is no domain given this is typically what is assumed but suppose that that's not the case. Suppose that instead we are given a very specific domain. We are told that this is only defined from negative three to five. Well graphing this is essentially no different than graphing a parabola that is defined in all real numbers, simply start plugging in some values that lie in this range and then connect the dots as we always do. So let's start by plugging in X equals zero, so if X equals zero here, this term becomes zero, we end up with negative five, go ahead and put it down here. Okay, X equals one, we get three minus five is negative two, somewhere around there and negative one we get three minus five, negative two again and we see that this is going to be symmetric for the most part. The only difference being that the right side will go out farther than the left side because our domain extends farther towards the positive than it does towards the negative. So you could go ahead and compute more of the numbers but essentially it's going to look something like this. Whenever you get to X equals negative three, instead of drawing an arrow at the end like we would normally do, you simply draw an endpoint and same thing over here for X equals five, that would probably be above the chalkboard. That's all there is to it. My name is Ryan Malloy and we just discussed how to graph a parabola that ends.


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