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Question 548555: find the focus of a parabola represented by the equation f(x)=x(squared)-8x+12 with the vertex at (4,-4).
Answer by lwsshak3(11628)   (Show Source):
You can put this solution on YOUR website! find the focus of a parabola represented by the equation f(x)=x(squared)-8x+12 with the vertex at (4,-4)
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f(x)=x(squared)-8x+12
y=x^2-8x+12
complete the squareS
y=(x^2-8x+16)+12-16
y=(x-4)^2-4
(x-4)^2=(y+4)
This is an equation for a parabola of the standard form: (x-h)^2=4p(y-k), with (h,k) being the (x,y) coordinates of the vertex. Parabola opens upward.
For given equation:
vertex: (4,-4)
Axis of symmetry: x=4
4p=1
p=1/4
Focus is located p units above the vertex on the axis of symmetry
Focus: (4,-4+1/4)=(4,-15/4)
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