Okay so, I'm going to explain how to do parabolas.

There are 5 easy steps in working out parabolas. These steps are:

1. The first thing you would do is look at the problem. Lets use two different problems as an example, one with y= and one with x=. This way you can understand it both ways. The first example is going to be (example 1)y=2x^2 and the other example is going to be (example 2)x=-2y^2. The first thing your going to do is look if there is an x or y being squared. In the first example you have a x being squared, where as in the second example you have a y being squared. Since in the first example you have a positive x being squared, you are know going to know that the parabola is going to go upwards. If you were to have a negative x being squared then you would know the parabola would be going down. Now, in the second example you have a negative y being squared, this lets you know that the parabola is going to go to the left. If you were to have a positive y then your parabola would face the right.
2. The second step would be to find the axis of symmetry. The equation to find this is x=-b/2a or y=-b/2a. This equation is going to depend on the problem you are working. If your probelm is like example 1 then you are going to use the x= equation and vice versa. So for example, if you were working example 1 and got x=h, the h would now go in point form (h, ?) The x-coordinate is never going to change throughout the whole problem. Now if you were working example 2 and got y=d, you would have (?, d) and that means the y-coordinate is never going to change throughout the whole problem.
3. The next thing you want to do is to try and find the missing coordinate. This step is very easy. All you do is plug in what you got for the step above into the equation. So for example, if you were on example 1, where you got x=h, you would then plug h into the equation which would be y=2(h)^2. Whatever you would get for that would be your other coordinate. So lets just say you got w. Your vertex would then be (h, w). The same goes for the other example, you would just switch up the x and y.
4. This next step is to find the focus. To find the focus you need to use the equation 1/4p=coefficient of leading term. So lets use example one, the leading term would be 2. So once you work that out, lets just say you got p=R So once you would get your answer, you would then add to your other vertex coordinate. REMEMBER: the one that you solved for in step 2 NEVER changes. So you would do (w+R) and whatever that would equal would be your focus. Vice versa goes for example 2.
5. The last step is going to find the directrix. This step is really easy. You would do the other vertex coordinate - p and that is going to equal the directrix. You would then write whatever you got for that as y=the # or vice versa for a x= problem.

Note: The vertex is going to be right in the middle of the focus and directrix.

Now, I'm going to work out a full example for you. I'm going to number the steps in my work to match the ones above.

EXAMPLE: y=-2x^2

1. The parabola is going to go downwards.
2. x=-0/2(-2), which is going to be x=0.
3. y=-2(0)^2, which is going to be y=0. You are then going to have a vertex of (0,0).
4. 1/4p=-2. Your going to multiply 1/4p to both sides, getting -8p=1, which then gives you p=-1/8. You would then do 0+(-1/8)=-1/8. The 0 you add is going to be the one that doesn't change the whole problem which is the y-coordinate. Your focus is then going to be (0,-1/8).
5. 0-(-1/8)=1/8. Which would then give you y=1/8. Which is going to be your directrix.

This is what the graph is going to look like:

And that's how you work parabolas.

Halie (: