SOLUTION: A person jumps from a spring diving board. The trajectory of the person off the diving board is represented by the function below. h(t) = -(x-1)^2 +4 where h is the height of the

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Question 522396: A person jumps from a spring diving board. The trajectory of the person off the diving board is represented by the function below.
h(t) = -(x-1)^2 +4
where h is the height of the person above the water and x is the distance the person is out from the diving board.
a) graph the function over the domain 0<_ x <_ 6
b) state the height of the diving board and state why you reached your conclusion
c) determine using algebraic procedures, the greatest height reached by the person and state at what distance the person was from the end of the board when the greatest height was reached.
thanks :)
Answer by solver91311(24713) (Show Source):
You can put this solution on YOUR website!

Graphing over the given interval is silliness since he hits the water at x = 3, and he certainly isn't going to continue along his parabolic path to a depth of 21 feet after that. Be that as it may: Choose integer values from 0 to 6, plug them into your function one at a time to calculate the function valuie for that x value, create an ordered pair each time, plot the ordered pair, and finally draw a smooth curve through your points.

If he is zero distance out from the diving board, he hasn't started the dive yet so he must still be on the board and his height must equal the height of the board. Look at the value of your function at for the answer to part b)

Since you have a parabola with a negative lead coefficient, the greatest height is the value of the function at the vertex. Having your function in vertex form is handy for this part of the question. A parabola with a vertex at has a vertex form equation of -- meaning your vertex is at the point

John

My calculator said it, I believe it, that settles it