Maximum of function [tex]f(x)=ax^2+bx+c[/tex] where [tex]a \neq 0[/tex] you can find by using this formula: [tex]y_{\max}= - \dfrac{\Delta}{4a}=-\dfrac{b^2-4ac}{4a}=\dfrac{4ac-b^2}{4a}=c-\dfrac{b^2}{4a}[/tex]
In height function you've got:
a= -16
b= 200
c= 4
Just substitute! You'll get
[tex]y_{\max} = 4 - \dfrac{200^2}{4 \cdot (-16)}=4-\dfrac{40 \ 000}{-64}=4+\dfrac{40 \ 000}{64}=4+625=629[/tex]
Maximum height is 629 [units]
