OK. So let's give this problem a try. So here we have the function F of X is equal to C times X squared. And we're asked to graph our function F of X when C is equal to two and when C is equal to one half, now what we have on the graph already here is a curve which represents our function F of X is equal to X squared. So this is the general for a parabola, but we need to figure out what's going to happen if we take various constants and plug it in to this function. So let's see. Well, we're going to start for the case where our constant here is equal to two. So this means that F of X is going to be two times X squared. This is what the function is going to look like if we plug two into for the constant. Now, what I'm going to do is try a bunch of different X values. So I'll first try an X value of zero. If this were to happen, we would have two times zero squared and two times zero is 00, squared is just zero. So that means we're going to have a point at 00, that's gonna be one point we can plot here. Now, what I'm also going to do is plot a value of negative one. If I do this, we're going to get two times negative one squared just replacing this X with a negative one. In this case, two times negative one is negative two. So we'll have negative two squared and negative two squared is actually positive four. So that means that a value of negative two or excuse me, a negative one, I mean a negative one, we're going to be at a Y value of four. So this is another point that we could put on this graph. Now lastly, I'm going to try a point of positive one. So in this case, we'll have two times one squared, two times one is two and two squared is four. So at a value of one, we're going to or at an X value of one, we're going to have a Y value of four. So our graph is going to look something like this when we replace this constant that we see here with a two. And I think this actually makes sense because recall in the previous video, we discussed whenever you have a constant multiplied inside of your function, it's going to cause a horizontal stretch or shrink to your graph. In this case, we saw the, it caused a horizontal shrink and this happens whenever your constant is greater than one. So it makes sense that we would get this situation where the graph shrinks since two is greater than one. But now let's try this other situation where we have one half. This basically means our constant is between zero and one. So let's see what happens if I do this. Well, in this case, our function F of X is going to become one half X squared because now we're just going to take this constant and replace it with the one half that we have over here. Well, let's see how this behaves. What I'm first going to do is plug in an X value of zero like we did before. In which case, we have one half times zero squared and anything multiplied by zero is just zero. So we already know this whole thing will come out to zero, meaning we'll have the same origin 0.00. Now, next, what I'm going to do is I'm actually going to try X value of two. And the reason that I'm trying two specifically is because if I take this X and replace it with a two and by the way, it doesn't actually matter, you could try one again, but you would just get a fraction. Um But if I go ahead and replace this with a two notice, we're going to get one half times two squared and one half and two will actually cancel each other here because taking two and cutting it in half will just give you one. So really, you just get up with one squared, which is just one. So if you try an X value you of positive two, you're going to end up here at a Y value of one. And likewise, if you were to try negative two, well, in this case, we would have one half times negative two squared. In which case, this two would cancel with that one giving us negative one squared and negative one squared is just positive one because negative one times negative one will cause the negative signs to cancel. So at an X value of negative two, we're going to be at a Y value of positive one. Again, meaning our function is going to look something like this. We multiply the inside by one half. And notice in this case, we got a horizontal stretch because whenever our constant is between zero and one, we get a horizontal stretch. Whereas when our constant is greater than one, we get a horizontal shrink. Now, one more thing I want to mention before finishing this video is notice that when we had the horizontal shrink, it almost appeared like we had a vertical stretch because in this situation where we had the horizontal shrink, it looked like vertically, the graph almost stretched and like w when we had a horizontal stretch, this kind of looked like we had a situation with a vertical compression or shrink. And that will often be the case when you see these types of graphs that have symmetry on them is that the horizontal stretches will oftentimes be similar to the vertical shrinks and the horizontal shrinks will be similar to the vertical stretches. So that's just something to keep in mind visually when looking at these graphs. But either way this is how you solve the problem and these are the answers. So hopefully you found this helpful, this is what the graph is going to look like.