00:01
This problem wants us to determine the equation for the parabola graph below, and for this parabola we're going to think of it as a quadratic, which we have because it's opening from a vertex down on both sides that's symmetric on the left and right.
00:13
And to begin building this function, we're going to start off with y equals a times x minus h squared plus k, which is a quadratic or a parabola in vertex form.
00:24
And the reason we're going to start off with this form is because we have the vertex, which is our h and k value.
00:29
So at this point we know that x minus h for the x minus h squared should be x minus negative 3, or x plus 3 squared.
00:37
And then our 4 is our k value, so that stays plus 4.
00:40
The other thing we need to determine is the a value, and one thing we can determine just from the general image of the graph is that since it's opening down, this a value is going to have to be a negative a for whatever it is.
00:52
And it could be an understood 1, but when we look at the stretch as far as how far down we're going from point to point, we have negative 3, 4 as a vertex, and normally to make the next point we would go right one unit, and then say what is 1 squared? 1 squared is 1, so we'd only go down one unit.
01:08
But that's not what we're seeing for our next point...