Answer:
C
Step-by-step explanation:
The given equation is a parabola:
h(t) = -16t²+64t+80
A. The rocket hits the ground in 2 seconds means that at the time t = 2 the height is h(2) = 0 since is on the ground.
h(2) = -16(2)²+64(2)+80
h(2) = -64 +128 +80
h(2) = 144 ≠ h(2) = 0 so A is FALSE
B. The maximum height of the rocket is 80 feet.
We have just seen that after 2 seconds the height was 144 feet so 80 feet cannot be maximum.
144 > 80 so 80 is not maximum height so B is FALSE
C. The maximum height of the rocket is 144 feet.
The maximum point is at point (2,144) so the maximum height 144 feet is reached after 2 seconds( see the graph.) C is TRUE
D. The rocket reaches its maximum height in 5 seconds.
This cannot be true since we established that C is true and a quadratic equation has only one min or max. D is FALSE
Option to calculate the max value algebraically:
h(t) = -16t²+64t+80
the x -coordinate is calculated as : -b/2a = -64/ 2(-16) = 2
the y-coordinate is calculated as: h(-b/2a) = h(2) = 144
point of maximum value ( 2, 144)
