Parabolas

A parabola is defined as a set of all points that are equidistant from a fixed line (directrix) and a fixed point (focus) not on the line. 

The point between the midpoint and the focus is called the parabola. Therefore we could calculate the vertex if we knew the focus and directrix. 

The equation of a parabola is:

For a parabola going up the vertices axis- (x-h)^2 = 4p (y-k) 

For a parabola going across the horizontal axis - (y-k)^2 = 4p (x-h) 

The vertex is (h,k) and the focus is always found by using p as well as the directrix.

Here's an example of how to find p.

If we wanted to find the focus, we know that the vertex is (-1,1). Since the parabola is going up, the value of x will remain the same and we will add the value of p to the y of the vertex. The directrix is subtracting it from the vertex.