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[help] Can't figure out how to complete a parabolic equation

Hey everyone!

I recently did a rocket project and I have the following things calculated (attached), however I'm supposed to get my data in the format:

y - k = a(x - h)^2

I figured out the height on my own by using tangent, but I'm not sure how to get it in the correct format.

Thanks for help in advance!

Re: [help] Can't figure out how to complete a parabolic equation

you have t = 6 seconds ... you need $\displaystyle \Delta x$ to get the parabola as a function of x

Re: [help] Can't figure out how to complete a parabolic equation

Could I somehow use points to figure that out? Since the vertex would be (3,33.12) and another point I could use would be the origin at (0,0)?

Re: [help] Can't figure out how to complete a parabolic equation

the vertex is not x = 3 , it is t = 3 ...

are you wanting the parabola as height vs. displacement or height vs. time?

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Re: [help] Can't figure out how to complete a parabolic equation

I asked my professor, and he just wants the flight path (which I'm guessing just the equation?)

This is what I have but I feel like something is way off when it comes down to the equation..

Re: [help] Can't figure out how to complete a parabolic equation

how far horizontally did the rocket land from where it was launched?

Re: [help] Can't figure out how to complete a parabolic equation

Another thing you can do is write your parabola in the general form $\displaystyle h= ax^2+ bx+ c$. You know that when x= 0, h= 0 so $\displaystyle 0= a(0)^2+ b(0)+ c= c$, that when x= 91, h= 0 so that $\displaystyle 0= a(91)^2+ b(91)+ c$, and that when x= 91/2= 45.5, h= 33.12 so that $\displaystyle 33.12= a(45.5)^2+ b(45.5)+ c$ (a parabola is symmetric so we know the vertex is half way between 0 and 91 feet). That gives three linear equations to solve for a, b, and c.