Answer:
The maximum height reached by the rocket is of 938.56 feet.
Step-by-step explanation:
The height y, after x seconds, is given by a equation in the following format:
[tex]y(x) = ax^{2} + bx + c[/tex]
If a is negative, the maximum height is:
[tex]y(x_{v})[/tex]
In which
[tex]x_{v} = -\frac{b}{2a}[/tex]
In this question:
[tex]y(x) = -16x^{2} + 230x + 112[/tex]
So
[tex]a = -16, b = 230, c = 112[/tex]
Then
[tex]x_{v} = -\frac{230}{2*(-16)} = 7.1875[/tex]
[tex]y(7.1835) = -16*(7.1835)^{2} + 230*7.1835 + 112 = 938.56[/tex]
The maximum height reached by the rocket is of 938.56 feet.
