00:01
In this problem, we are trying to essentially rearrange a quadratic function.
00:08
And in this case, a parabola using the vertex form or the standard equation for the vertex form of a quadratic function.
00:18
So what does this mean? we are going to have to use our knowledge of quadratics and use those values from that function and plug it into our standard equation.
00:29
So what is our standard equation? our standard equation looks like this.
00:34
We have x minus h squared is equal to a times y minus k, where we see that h comma k is a coordinate, and that coordinate is the vertex of our parabola, and a is the distance between the vertex and our point of focus.
00:54
So now what we need to do is rearrange our equation.
00:57
So we're going to say let y be our function, 5x squared minus 25x.
01:03
So the first thing we can do is factor out of 5.
01:05
And we can say that y equals 5 times x squared minus 5x.
01:11
So now this step is a little bit tricky.
01:14
This takes a little bit of clever rearrangement.
01:18
So we'll get 5 is equivalent, pardon me, y is equivalent to 5 times this entire quantity...