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Prove that the trajectory of a projectile is parabolic, having the form $y = ax + bx^2$. To obtain this expression, solve the equation $x = v_{ox}t$ for $t$ and substitute it into the expressions for $y = v_{oy}t - \dfrac{1}{2}gt^2$ (These equations describe the $x$ and $y$ positions of a projectile that starts at the origin.) You should obtain an equation of the form $y = ax + bx^2$ where $a$ and $b$ are constants.
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OpenStax College Physics Solution, Chapter 3, Problem 48 (Problems & Exercises) (1:39)

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