Question

An archers arrow follows a parabolic path. The height of the f(x) is given by f(x) =-16x^2+200x+4 in feet. Find the maximum height of the arrow

Answer 1

Maximum of function $f(x)=ax^2+bx+c$ where $a \neq 0$ you can find by using this formula: $y_{\max}= - \dfrac{\Delta}{4a}=-\dfrac{b^2-4ac}{4a}=\dfrac{4ac-b^2}{4a}=c-\dfrac{b^2}{4a}$

In height function you've got:

a= -16
b= 200
c= 4

Just substitute! You'll get

$y_{\max} = 4 - \dfrac{200^2}{4 \cdot (-16)}=4-\dfrac{40 \ 000}{-64}=4+\dfrac{40 \ 000}{64}=4+625=629$

Maximum height is  629  [units]