Answer:
y = 841.25 feet
Step-by-step explanation:
Given that,
The height of the rocket, y in feet, is  related to the time after launch, x in seconds, by the given equation as follows:
[tex]y = -16x^2 + 212x + 139[/tex] ....(1)
We need to find the maximum height reached by the rocket.
For maximum height, put dy/dx = 0
So,
[tex]\dfrac{d(-16x^2 + 212x + 139)}{dx}=0\\\\-32x+212=0\\\\x=\dfrac{212}{32}\\\\x=6.625\ s[/tex]
Pu x = 6.625 in equation (1).
[tex]y = -16(6.625)^2 + 212(6.625) + 139\\\\y=841.25\ feet[/tex]
So, the maximum height reached by the rocket is equal to 841.25 feet.
