Answer:
The rocket reached its maximum height at 2 seconds.
The maximum height of the rocket is 36 yards.
Step-by-step explanation:
Quadratic equation:
In the format
[tex]h(t) = ah^{2} + bh + c[/tex]
The maximum height happens at the instant of time:
[tex]t_{v} = -\frac{b}{2a}[/tex]
The maximu height is [tex]h(t_{v})[/tex]
In this question:
[tex]H(t) = -3t^{2} + 12t + 24[/tex]
So [tex]a = -3, b = 12, c = 24[/tex]
When did the rocket reach its maximum height?
[tex]t_{v} = -\frac{12}{2*(-3)} = 2[/tex]
The rocket reached its maximum height at 2 seconds.
What was the maximum height of the rocket?
H(2).
[tex]H(2) = -3*2^{2} + 12*2 + 24 = 36[/tex]
The maximum height of the rocket is 36 yards.
