00:01
Let's say we're given the following.
00:04
We're given the function f of x equals negative x squared minus 2x minus 3.
00:12
And let's say i want to find the vertex.
00:15
Well, there's an actual formula for finding the vertex.
00:18
I'm going to write it down.
00:19
It is negative b over 2a, comma, f of negative b over 2a.
00:27
All right.
00:28
And remember, this is a quadratic function.
00:30
So we could think of this as f of x is a x squared plus bx plus c.
00:38
So we're going to use those coefficients in order to find these values.
00:41
So let's begin first with finding the x value of the vertex.
00:47
So the x value of the vertex would be negative b.
00:51
So that would be negative negative 2 or the opposite of negative 2 over 2 times negative 1.
00:59
So we'll end up with 2 over negative 2, which is negative 1.
01:03
So so far for my vertex, i have a value of negative 1.
01:08
Then we want to find f of negative 1.
01:11
That's going to give us our y values.
01:14
So we'll substitute in negative 1 into our function.
01:19
And we're going to end up with negative 1 plus 2 minus 3, which will give us a value of negative 2.
01:29
My vertex is the point negative 1, negative 2.
01:34
Well, what about the axis of symmetry? and of course, we have a formula for that.
01:40
The axis of symmetry is x equals negative b over 2a.
01:45
Does that look familiar? well, it's the exact same as the x coordinate of the vertex.
01:51
So my axis of symmetry is the vertical line x equals negative 1.
01:58
Well, what about x intercepts? well, in order to figure out the x intercepts, we're going to look at, hey, when is f of x equal to 0? so let's go ahead and try to solve that...