00:02
So if we first want to find the value of c in our quadratic here, well, this is just our y intercept.
00:13
Because what this is really saying is if we were to plug in zero for x, y is equal to c, which is the y intercept.
00:21
So our y intercept is just going to be 10.
00:24
So c is equal to 10.
00:28
So let's just come over here and plug that in now.
00:34
So we have that.
00:37
Now, we also know that one of the x intercepts is one, and the x coordinate of the vertex of the graph is three.
00:51
So let's go ahead and put this into vertex form instead.
00:56
So let's look at y is equal to.
00:58
Well, now this a is going to be the same a as this one.
01:01
And then it'd be x minus.
01:04
Well, the x coordinate of the vertex is 3.
01:09
So actually, let's just write this out first like that.
01:14
So h here is the x coordinate for our vertex, because our vertex will look something like hk like that.
01:26
So we can come over here and replace this with 3.
01:32
Because over here they say the x -quartagnet, is i don't know why it highlighted it like that.
01:43
Now with this in mind, we can try to solve for what a and k are using the fact that we know that the y intercept is 0 and also that the x, one of the x intercepts is 1.
02:05
So what we really have right now, so we have the y intercept, which is going to be the 0 .010.
02:11
And then we also have one of the x intercepts is 1, which means the point 1, 0.
02:16
So we can plug these into here, and we'll end up with an equation we can solve.
02:22
So let's go ahead and do that for both of these.
02:28
So when we plug in x is equal to 0, y is equal to 10, we get 10 is equal to a times.
02:35
So that would just be 0 minus 3.
02:40
So that would just be negative 3 squared plus k.
02:45
And then that's going to be 9.
02:46
So we have 10 is equal to 9a plus k.
02:53
And then if we plug in 1 and 0 over here, we know if 0 is equal to a times 1 minus 3 squared plus k...