Question

Since the balll is at a height of 0 feet at x=0 and x=70, then the maximum height is archieved at x=35.Use the function rule to determine that maximum height and confirm it on the graph.h(x) = -0.03x (x-70)

Answer 1

The maximum height refers to the vertical coordinate of the vertex V(h,k), where

$h=-\frac{b}{2a}$

According to the given equation, we have the following

$h(x)=-0.03x(x-70)=-0.03x^2+2.1x$

Where a = -0.03 and b = 2.1

$h=-\frac{2.1}{2\cdot(-0.03)}=\frac{2.1}{0.06}=35$

Then, we find k by evaluating the function when x = 35.

$h(35)=-0.03\cdot35(35-70)=-1.05(-35)=36.75$

Hence, the maximum height is 36.75 feet.