ACT Math 4.4 Coordinate Geometry
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ACT Math: Coordinate Geometry Drill 4, Problem 4. Find the vertex.
|ACT Math||Coordinate Geometry|
|ACT Mathematics||Coordinate Geometry|
|Algebra||Coordinates and Graphs|
|Coordinate Geometry||Conic sections|
|Foreign Language||Arabic Subtitled|
|Product Type||ACT Math|
y = a(x -- h) squared + k.... where the vertex is (h,k)
The k is gonna be all about how high or low the vertex of the parabola sits along the y
A vertex is this base point on the parabola.... its absolute bottom or top or... side thing.
So now we have this equation that they give us:
and we have to put it into standard form.
We can first subtract 1 from both sides and then factor out the 2 on the right to get
y minus 1 equals 2 times quantity x squared minus 2x.
We can now complete the square inside the parentheses...
Given x squared plus bx...we can
complete the square by adding the quantity b over 2 squared...
In this case, when we look at x squared minus 2x in the parentheses...b is negative 2..so
negative 2 divided by 2 is negative 1...and negative 1 squared is 1.
But remember, we've just completed the square in the parentheses...so we're actually adding
2 to the right side...which means we have to add 2 to the left side as well.
The right side simplifies to 2 times the quantity x minus 1 squared...and the left side simplifies
to y plus 1. We can now subtract 1 from both sides... and we see that the equation is in standard form!
We see that h is 1 and k is negative 1. So our vertex is (1, -1).