SOLUTION: Find the coordinates of the vertex of the parabola y=x2-4x+1 by making use of the fact that at the vertex, the slope of the tangent line is zero.

Algebra ->  Test -> SOLUTION: Find the coordinates of the vertex of the parabola y=x2-4x+1 by making use of the fact that at the vertex, the slope of the tangent line is zero.      Log On


   

Question 942469: Find the coordinates of the vertex of the parabola y=x2-4x+1 by making use of the fact that at the vertex, the slope of the tangent line is zero.
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
It's easier to just complete the square but ...
The slope of the tangent is also the value of the derivative.
y=x%5E2-4x%2B1
dy%2Fdx=2x-4
Set this equal to zero.
2x-4=0
2x=4
x=2
So then,
y=a%28x-2%29%5E2%2Bb
y=a%28x%5E2-4x%2B4%29%2Bb
y=ax%5E2-4ax%2B4a%2Bb
Comparing to the original equation,
-4a=-4
a=1
Then,
4a%2Bb=1
4%2Bb=1
b=-3
So the equation in vertex form is,
y=%28x-2%29%5E2-3
and the vertex is (2,-3)
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graph%28300%2C300%2C-5%2C5%2C-5%2C5%2Cx%5E2-4x%2B1%29