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 ______

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

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
Answer by math_tutor2020(3817)   (Show Source): You can put this solution on YOUR website!
Answers
The rocket splashed down after     46.15603   seconds.
The rocket peaks at     2825.5   meters above sea level.

Explanation
Use the quadratic formula 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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