Graph of Quadratic describes Parabola/Corollary 1

Theorem
The locus of the equation of the square function:
 * $y = x^2$

describes a parabola.

Proof
This is a particular instance of Graph of Quadratic describes Parabola, where:
 * $y = a x^2 + b x + c$

is the equation of a parabola.

The result follows by setting $a = 1, b = 0, c = 0$.