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viktelen [127]
2 years ago
15

The equation h(t) = –16t2 + 64t + 80 models the height of a rocket launched from the top of a building. Which statement is true?

Mathematics
2 answers:
Travka [436]2 years ago
7 0

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)

Ostrovityanka [42]2 years ago
6 0

Answer:

the maximum height of the rocketis 144 feet

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