SOLUTION: y=4x^2+4x+9

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Question 1192762: y=4x^2+4x+9
Answer by josgarithmetic(39618) About Me  (Show Source):
You can put this solution on YOUR website!
What do you want help to do?
Graph? Find roots? Equation manipulation into another form?

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Okay now you need to edit your question post.


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y=4%28x%5E2%2Bx%29%2B9
y=4%28x%5E2%2Bx%2B%281%2F2%29%5E2%29%2B9-4%281%2F2%29%5E2
y=4%28x%2B1%2F2%29%5E2%2B9-1
highlight_green%28y=4%28x%2B1%2F2%29%5E2%2B8%29
This tells you that the vertex of this vertical-axis parabola is at (-1/2, 8).

The inverse of the parabola is either for this parabola's left branch or for this parabola's right branch. The inverse will have a left most point
at (8, -1/2).

For inverse, a quick way is to simply switch x and y and solve for y.
4%28y%2B1%2F2%29%5E2%2B8=x
4%28y%2B1%2F2%29%5E2=x-8
%28y%2B1%2F2%29%5E2=%28x-8%29%2F4
y%2B1%2F2=0%2B-+sqrt%28x-8%29%2F2
highlight%28y=-1%2F2%2B-+sqrt%28x-8%29%2F2%29-------You'll have to choose which part you want here: the PLUS or the MINUS.