A parabola represents the locus of points in a plane that are equidistant from a fixed point and a specific line. The fixed point described is called the locus, while the specific line the directrix.
A parabola is symmetric about the line perpendicular to the directrix through the focus. This line is called axis of symmetry.
P (x,y) will simbolize be any point in the parabola.
V (h,k) represents the vertex.
The Axis of Symmetry will be aline where two sides of the parabola will look like a exact images of each other.
4p is the length of the parabola.
2p will be how much the parabola opens to one side and to the other.
p is the distance from the vertex to the focus and to the directrix. The type of parabola will determine where your focus and directrix are located; whether you move p units up or down, or p units left or right.
Here are the two types of parabola, vertical and horizontal, with their negative and positive aspects.
How to solve for a parabola from general to standard form
Formula for Perfect Squares
To solve for a parabola in general form, we have to complete the square. Lets assume we have an equation such as the one presented in problem a of Figure 2. First, the 4 is passed to the right side, so the equation becomes equal to 4, not 0. Then, we must complete the square in order to simplify the equation. To do this, b of the general form, which in this case is 8, is divided by two. Whatever the result, in this case 4, it must be squared. The value that results from the square, in this case 16, must be added to the left part in order to complete the square. However, if you add or subtract something from one side of the equaiton, you have to do the same to the other side, so, the 16 is added to the right side too. Now the equation is equal to 20. The trinomial on the left side is a perfect square, so simplified, it will become (x+4)2 . This will be the standard formula for the parabola. It is plausible for this to happen even though it does not show any y. Why? Because in this case, y and k equal 0.
Figure 3 shows another example of how to convert a parabola equation from general to standard form.
How to Graph a Parabola
Video on how to graph a parabola, click to watch.
The Conic Club 