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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.
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:
Full Transcript
- 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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