Throw a ball straight up at $v_0$ — v-nought, the launch speed — and its height follows $h = v_0 t - \tfrac{1}{2} g t^2$. Read aloud: h equals v-nought t minus one-half g t-squared, with $g = 9.8\ \mathrm{m/s^2}$, gravity's tax rate. Look hard at that formula: it IS $y = ax^2 + bx + c$ wearing physics clothes — a = −4.9, b = v₀, c = 0. Everything this chapter taught now works on the sky: the apex is the vertex, the landing is a root.

Two shortcuts fall straight out: the peak is $H = \dfrac{v_0^2}{2g}$ and the full flight lasts $T = \dfrac{2 v_0}{g}$ — up takes $v_0/g$, and the fall politely takes the same. Run the units as a guide, never a confession: $\mathrm{(m/s)\cdot s = m}$ and $\mathrm{(m/s^2)\cdot s^2 = m}$ — every term in a height equation must BE a height, or the equation is lying.