Question 1204519
<font color=red>Answers</font>
The rocket splashed down after <u>&nbsp;&nbsp;&nbsp; <font color=red>46.15603</font>&nbsp;&nbsp;</u> seconds.
The rocket peaks at <u>&nbsp;&nbsp;&nbsp; <font color=red>2825.5</font>&nbsp;&nbsp;</u> meters above sea level.


Explanation
Use the quadratic formula {{{t = (-b+-sqrt(b^2-4ac))/(2a)}}} to find the two roots are approximately t = -1.87032 and t = 46.15603
I'll let the student do the steps and scratch work for the quadratic formula.
We ignore the negative t value.
The positive t value is when the rocket splashes into the ocean.



The average of the roots is approximately (-1.87032+46.15603)/2 = 22.142855
This is the axis of symmetry. It's when the rocket reaches its highest point.
Plug this t value into the h(t) function to find that h(22.142855) = 2825.5
The vertex is at the approximate location (22.14284, 2825.5)
The rocket's highest point is approximately 2825.5 meters.
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