Finding "a" in a parbola?

Question

Using this equation,(y=a(x-h)^2+k). Howd do I write an equation of a parabola. I know that for h and k you use the vertex cordinates. How do I find a?

Answer 1

you need one more point (x,y). Then substitute (h,k) and (x,y) in the equation (called vertex form) and solve for a.

Answer 2

The equation you show is the general equation for a parabola. As you have noted, (h, k) offsets the vertex of the parabola from (0,0). The factor a in the equation alters the "flatness" of the parabola. If a = 1 then you have the "basic" parabola. As a decreases below 1, you get a flatter parabola but it is still a parabola. Similarly as a increases above 1 you get a steeper and narrower parabola.

I have made a quick and dirty graph to show the effect of changing "a" in the formula (I ignored h and k). As you can see, changing a changes the flatness of the parabola and the focus of the parabola, but they are still parabolas.

http://img216.imageshack.us/my.php?image...

You may want to add more detail to your question, I'm not sure that I answered what you are wanting to ask.