[tex]\large\textsf{Quadratic equation:}~~\fbox{$\mathsf{ax^2+bx+c}$}\\\\\\\mathsf{When~a\ \textless \ 0~the~parable~have~concavity~\underline{downward}~and~have~one~max}\\\mathsf{point.}\\\\\\\mathsf{The~max~point~is~a~vertex~of~the~parable~and~its~coordinates~are}\\\mathsf{obteined~by:}\\\\\\\mathsf{x~of~vertex~X_v=\dfrac{-b}{2a}}\\\\\\\mathsf{y~of~vertex~Y_v=~\dfrac{-\Delta}{4a}}\\\\\\\mathsf{For~this~question~we~must~find~the~Y_v.}[/tex]
[tex]\mathsf{-16t^2+48t-20}\\\\\\\mathsf{coefficient~a=-16;}\\\mathsf{coefficient~b=48;}\\\mathsf{independent~term=-20.}[/tex]
[tex]\mathsf{Y_v=\dfrac{-\Delta}{4a}}\\\\\\\mathsf{\Delta=b^2-4ac}\\\\\\\mathsf{\Delta=48^2-4\cdot(-16)\cdot(-20)}\\\\\\\mathsf{\Delta=2304-1280}\\\\\\\mathsf{\Delta=1024}\\\\\\\mathsf{Y_v=\dfrac{-1024}{4\cdot(-16)}}\\\\\\\mathsf{Y_v=\dfrac{-1024}{-64}}\\\\\\\fbox{$\mathsf{Yv=16}$}~~~~\checkmark[/tex]
[tex]\textsf{So~the~maximum~height~of~the~child's~bounce~is~16.}[/tex]
