Vive la Parabole! (My Favorite Conic Section)

You can keep your polynomials
And cosine waves galore.
But did you say 'parabola?'
Well, then, say no more.
Parabolas are elegant;
Parabolas are neat.
Their graceful and yet simple curve
Will sweep you off your feet.
They have no messy a's or b's
And thankfully, no c.
The only fraction present is
One over four P.
Parabolas are wonderful;
Parabolas are nice.
Their equation's understandable
And can be quite concise.
If the coefficient's negative,
It makes a frowny face.
If it's positive, however,
It has a vague U-shape.
Parabolas are marvelous;
Parabolas are fun.
I quite enjoy quadratics,
As should everyone.