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ACT Math 4.4 Coordinate Geometry 305 Views


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Description:

ACT Math: Coordinate Geometry Drill 4, Problem 4. Find the vertex.

Language:
English Language

Transcript

00:02

For a good time, solve this shmoopy question.

00:04

Find the vertex of the parabola  y = 2x squared -- 4x + 1.

00:09

And here are your potential answers...

00:14

...do we know the standard form formula?

00:16

Well, if we were in class that day... ahem...we'd know that its form is:

00:22

y = a(x -- h) squared + k.... where the vertex is (h,k)

00:27

The k is gonna be all about how high or low the vertex of the parabola sits along the y

00:33

axis direction.

00:34

A vertex is this base point on the parabola.... its absolute bottom or top or... side thing.

00:40

So now we have this equation that they give us:

00:42

and we have to put it into standard form.

00:45

We can first subtract 1 from both sides and then factor out the 2 on the right to get

00:50

y minus 1 equals 2 times quantity x squared minus 2x.

00:55

We can now complete the square inside the parentheses...

00:57

Given x squared plus bx...we can

00:59

complete the square by adding the quantity b over 2 squared...

01:03

In this case, when we look at x squared minus 2x in the parentheses...b is negative 2..so

01:09

negative 2 divided by 2 is negative 1...and negative 1 squared is 1.

01:15

But remember, we've just completed the square in the parentheses...so we're actually adding

01:20

2 to the right side...which means we have to add 2 to the left side as well.

01:23

The right side simplifies to 2 times the quantity x minus 1 squared...and the left side simplifies

01:29

to y plus 1. We can now subtract 1 from both sides... and we see that the equation is in standard form!

01:36

We see that h is 1 and k is negative 1. So our vertex is (1, -1).

01:42

Answer's (B).

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