The trajectory of a projectile in a vertical plane is y = - β x ^ 2...

$y = \alphax - \beta{x}^{2}$
comparing with trajectory equation

$y = xtan\theta - \dfrac{1}{2}\dfrac{g{x}^{2}}{{u}^{2}\cos^{2}\theta}$

$tan\theta = \alpha ⇒ \theta = \tan^{- 1}\alpha$

$\beta = \dfrac{1}{2}\dfrac{g}{{u}^{2}\cos^{2}\theta}$

${u}^{2} = \dfrac{g}{2\beta\cos^{2}\theta}$

Maximum height : $H$

$H = \dfrac{{u}^{2}\sin^{2}\theta}{2g} = \dfrac{g}{2\beta\cos^{2}\theta}\dfrac{\sin^{2}\theta}{2g}$

$H = \dfrac{\tan^{2}\theta}{4\beta} = \dfrac{{\alpha}^{2}}{4\beta}$