I'm confused why my teacher is using a different form than the book of the standard equation of a parabola.

Teacher: y - k = (1/(4d))(x-h)^2

Book: (y - k)^2 = 4p(x - h), p != 0

Are the two equations the same? Any help is appreciated. Thanks!

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- April 19th 2011, 05:42 PMArcherSamStandard Equation of a Parabola
I'm confused why my teacher is using a different form than the book of the standard equation of a parabola.

Teacher: y - k = (1/(4d))(x-h)^2

Book: (y - k)^2 = 4p(x - h), p != 0

Are the two equations the same? Any help is appreciated. Thanks! - April 19th 2011, 05:47 PMjohnny
Multiply both sides of the equation by 4d, i.e. (x - h)² = 4d(y - k). If d < 0, then the graph opens down, and if d > 0, then the graph opens up.

If p < 0, then the graph opens left, and if p > 0, then the graph opens right. - April 20th 2011, 11:20 AMArcherSam
Thanks! So the two equations are equal. [:)]

Solution give by johnny!:

y-k = (1 / (4d))(x -h)^2

(4d / 1)(y - k) = (4d / 1)(1 / (4d))(x - h)^2

(x - h)^2 = 4d(y - k)