Thread: Standard 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!

Originally Posted by ArcherSam

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

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.

Originally Posted by ArcherSam

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

If p < 0, then the graph opens left, and if p > 0, then the graph opens right.

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)