SOLUTION: nasa launches a rocket at t=0 seconds. its height, in meters above sea-level,as a function of time is given by h(t)=-4.9t^2+217t+423 The rocket splashed down after _______ seconds

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Question 1204519: nasa launches a rocket at t=0 seconds. its height, in meters above sea-level,as a function of time is given by h(t)=-4.9t^2+217t+423
The rocket splashed down after _______ seconds.
The rocket peaks at _____ meters above sea level
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Answers
The rocket splashed down after     46.15603   seconds.
The rocket peaks at     2825.5   meters above sea level.

Explanation
Use the quadratic formula t+=+%28-b%2B-sqrt%28b%5E2-4ac%29%29%2F%282a%29 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.