SOLUTION: what is the standard form of y^2= -4y+2x+1?

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Question 822060: what is the standard form of y^2= -4y+2x+1?
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
y is squared, x is only power 1. This is a horizontal parabola. You want a finished form like x=a%28y-k%29%5E2%2Bh, and you find it through completing the square for the y.

y%5E2=+-4y%2B2x%2B1
y%5E2%2B4y-1=2x
2x=y%5E2%2B4y-1
The missing square piece, or term, is 4.
2x=y%5E2%2B4y%2B4-4-1
2x=%28y%2B2%29%5E2-5
highlight%28x=%281%2F2%29%28y%2B2%29%5E2-5%2F2%29

The formula for x could have been found without leaving the 2 factor with the x, but keeping the 2x allowed an easier completion of the square process.