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how do you find p when trying to find the focus for parabolas

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1 Answer

It depends on what kind of information you are given, and what kind of parabola (vertical or horizontal) you have.

If you have a vertical parabola you can get it to be in the the form (x - h)= 4p(y - k) by completing the square. Then the vertex is (h, k) and the focus is (h, k + p). Since it's a vertical parabola, we change the y-coordinate of the vertex.

If you have a horizontal parabola, of the form (y - k)2  = 4p(x - h), vertex is (h, k) so focus is (h + p, k). (Since parabola is horizontal, the focus is related to the x-coordinate of the vertex.)

That's a super general answer, but I hope it helps for now.

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