Question

PLEASE HELP
A ball is thrown into the air from a height of 6 ft. The height, h, of the ball after t
seconds, is given by the equation h= -4.9+2 + 40t + 6. What is the maximum height
the ball reaches?
between 70 ft and 75 ft
between 75 ft and 80 ft
over 85 ft
between 80 ft and 85 ft

Answer 1

Answer:

Over 85 ft

Step-by-step explanation:

The maximum height of the ball is going to be located at the vertex of the parabola. First you need to find the x (or t in this case) coordinate for the axis of symmetry. Using the equation for the axis of symmetry of a parabola:

$x=\frac{-b}{2*a}$

$t=\frac{-40}{2*(-4.9)}=\frac{-40}{-9.8}=4.0816$

After finding the t-coordinate for the vertex, then plug this value into the original equation to find the corresponding h-coordinate:

Assuming the equation is $h=-4.9t^{2}+40t+6$,

$h=-4.9(4.0816)^{2}+40(4.0816)+6=-81.6313+163.264+6=87.6327$

So the vertex can be represented as (4.016, 87.6327)

The maximum height is over 85 ft.