SOLUTION: what is the vertex, focus, and directrix of y=1/3x^2-2x+6

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Question 443938: what is the vertex, focus, and directrix of y=1/3x^2-2x+6
Answer by poliphob3.14(115) About Me  (Show Source):
You can put this solution on YOUR website!
First we need to find the standard form of the parabola equation:
3y=x%5E2-6x%2B18 => x%5E2-6x%2B9=3y-9 => %28x-3%29%5E2=3%28y-3%29.
The final equation is the equation of parabola with vertex (3, 3).
Since 4c=3 we get c=3/4, and the focus is (3, 3+3/4) or (3, 15/4).
The directrix is y=3-3/4=9/4.
graph%28600%2C+600%2C+-10%2C+10%2C+-10%2C+10%2C+%281%2F3%29x%5E2-2x%2B6%29