Question #05734

1 Answer
Aug 21, 2016

#5# feet

Explanation:

Take a look at the graph of this equation.
graph{-16x^2+8x+4 [-10, 10, -5, 5]}

We can see that the maximum height of the object occurs at the vertex of the parabola. In order to find the time #t_max# where the object reaches the vertex, we can use the following formula:
#t_max=-b/(2a)#

This is the formula used throughout algebra to find the #x#-coordinate of the vertex of a parabola.

In the equation #-16t^2+8t+4#, we have #a=-16# and #b=8#, so:
#t_max=-(8)/(2(-16))=1/4# seconds

This tells us that the maximum height of the object is reached at #t=1/4# seconds. However, the question asks for the actual height, not the time. To find the height, we simply plug in #1/4# for #t#:
#S(t)=-16t^2+8t+4#
#S_max(t)=S(t_max)=S(1/4)=-16(1/4)^2+8(1/4)+4#
#=5# feet