Hi guys! I'm Nancy.
And today we're going to talk about how to
find the vertex of a parabola.
So the first thing you'll need to know is
if you've been given the standard form of
the parabola, or the vertex form of the parabola.
Say that you've been given the standard form
of the equation of a parabola. Such as Y equals
-2X squared plus 4X plus 1.
Now that is the standard form, which in general
looks like Y equals A X squared plus B X plus
C.
So in your case, your A is -2, your B is 4
and your C is 1.
Now for the vertex, all you need to remember
is the formula -B over 2A.
It's really all you need. -B over 2A.
So in this problem, -B over 2A is equal to
-4 over 2 times -2. Which turns out to be
-1 over -1, or just positive 1.
OK, so what trips people up in finding the
vertex is that they don't know the equation.
So if you can remember -B over 2A, then you're
set. That will give you the vertex.
So all you need to do is remember the formula
-B divided by 2A.
So now you have 1, which is your X coordinate
in your vertex pair. So you're halfway there.
That was actually the hard part.
And all you have to do is take that 1, that
X, and plug it in for X and plug it in for
X in your original equation.
So here that means, Y = -2 times 1 squared
plus 4 times 1 plus 1.
And that simplifies to -2 plus 4 plus 1, which
equals 3.
So now you know that the Y coordinate in your
vertex is 3.
So your vertex is the point 1, 3.
OK, so now we're gonna look at the vertex
form, which is great cause it's super easy!
As if you needed another form.
But this one is actually a lot easier, because
if you're given this form, you can literally
pull the vertex coordinates straight from
the equation.
The vertex form in general looks like Y equals
A times X minus H squared plus K.
And all you need to know is that H, K is your
vertex.
So it really is just pattern matching. You
want to match H and K to the numbers that
you were given.
If it was minus H in the general equation,
and minus 1 in your example, then you H equals
1. And your K equals 3.
So the vertex for this problem would be H,
K or 1, 3.
And that's it.
So sometimes the signs are a bit more confusing,
so I'm going to show your another one.
So remember the vertex form looks like this.
So if you are given an equation
that instead has an X plus a number
inside the square,
all you'll need to do is rewrite it so that
it's in the X minus form.
So we would have 2 times X minus a negative 3.
Since minus a negative is the same as plus -- plus 3.
So now you can see to match it to the vertex
form, H has to be -3.
So the vertex in this case would have an X
value of -3.
And a Y value that is K.
Which is simply positive 4.
So our point, our vertex, is -3, 4.
OK guys, so I hope that helped you figured
out how to find the vertex of a parabola.
If you like this video, click 'Like' and let
me know!
