Question

Is "y=-0.00635x^2+4.0005x" in the correct form to be a Parabola

Answer 1

Yes.

Any parabola is represented by an appropriate second degree polynomial, which means that to identify a particular parabola you have to choose three coefficients $a,b,c, \in \mathbb{R}$ to identify the polynomial

$ax^2+bx+c$

In your case, the expression $-0.00635x^2+4.0005x$ comes from the choice $a = -0.00635, b = 4.0005, c=0$, and so by all means its graph is a parabola.