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 $a = 1, b = 0, c = 0$.

$\blacksquare$

Sources

• 2008: Ian Stewart: Taming the Infinite ... (previous) ... (next): Chapter $6$: Curves and Coordinates: Functions