I am creating a project for math in which I have to draw an object using: parabolas, hyperbolas, circles,etc.

Question

We use conic section equations to identify where they are on the graph.

I have confusion about writing the equation of parabolas. I know the equation is 4px=y^2 but I can't find p because I don't know were the focus point is. I drew parabolas, how would I find the focus point (or directrix) to help me find p for the equation?

note: they don't give you an equation you need to make one yourself.

my vertex (11,3)

Answer 1

if the coefficient of x^2 is positive, the parabola will go up. Otherwise, it will go downwards