SOLUTION: Explain how you would change the equation x ^ 2 - 4y - 4x + 24y = 36 into standard form, show all steps and identify the conic.

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Question 746995: Explain how you would change the equation x ^ 2 - 4y - 4x + 24y = 36 into standard form, show all steps and identify the conic.
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
x+%5E+2+-+4y+-+4x+%2B+24y+=+36

x%5E2-4x%2B24y-4y=36
x%5E2-4x%2B20y=36
20y=-x%5E2%2B4x%2B36
y=-%281%2F20%29x%5E2%2B%281%2F5%29x%2B36%2F20
y=-%281%2F20%29x%5E2%2B%281%2F5%29x%2B9%2F5, this is a parabola with a maximum. y on one side is degree 1 and there is x^2 term meaning x to degree 2.

Use Completing of the Square to put into standard form:
y=-%281%2F20%29%28x%5E2-4x%29%2B9%2F5
y=-%281%2F20%29%28x%5E2-4%2B4%29%2B9%2F5-%284%29%28-1%2F20%29-------this is the adding and subtracting of the missing square term.
y=-%281%2F20%29%28x-2%29%5E2%2B9%2F5%2B1%2F5
highlight%28y=-%281%2F20%29%28x%5E2-2%29%2B2%29--------Standard Form