Answer:
The maximum height 400 feet is attained at t = 5 seconds.
Step-by-step explanation:
All powers of in the equation for are integers that are greater than or equal to zero. Additionally, the greatest power of is two. Hence, is a quadratic equation about .
- Let be the coefficient of the term, and
- Let be the coefficient of the term.
In this case,
- , and
- .
The question is asking for the maximum value of this equation. Start by finding the (time) that would maximize the value of the polynomial.
The graph of a quadratic equation looks like a parabola. Additionally, since the coefficient of is less than zero, the parabola opens downward. The maximum value of the parabola would be at its vertex. Additionally, at the vertex,
.
In other words, the rocket is at its maximum height when time is equal to 5 seconds.
To find that height, let and evaluate :
.
That is: the maximum height of the rocket would be 400 feet.