Question 1025681: I have collected data has follows for a projectile we threw in class:
Estimated launch height - 1.0m
Estimated max height - 2.6m
Estimated horizontal distance traveled - 6.4m
flight time - 1.33s
With this data, I want to make an equation in vertex form - y=a(x-h)2+k
Where y is the vertical distance traveled and x is the horizontal distance traveled. How would I complete the equation with that information?
Answer by solver91311(24713)   (Show Source):
You can put this solution on YOUR website!
Since height as a function of time is given by:
\ =\ -4.9t^2\ +\ v_ot\ +\ h_o)
where  is the initial VERTICAL velocity and  is the initial height, you can plug in your value for the total flight time,  and a \ =\ 0) (since that was the height at the end of the 1.33 seconds), and then calculate .
\ =\ -4.9(1.33)^2\ +\ v_o(1.33)\ +\ 1\ =\ 0)
Once you have , and recalling that the  -coordinate of the vertex of  is given by  , you can calculate the horizontal displacement of the highest point by:
Then, plugging values into your vertex form of a parabola, you get
^2\ +\ 2.6)
The only thing left to do is find an appropriate value for a.
Since we know that when the horizontal displacement was zero, the vertical displacement was 1, so:
^2\ +\ 2.6)
Solve for 
I left all of the arithmetic for you to do yourself. Enjoy.
John
My calculator said it, I believe it, that settles it
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