Thread: Finding a Parabolic equation with imaginary points?

I know this is a really off the wall question, and I don't know where else to put it so here goes:

For the past 2 months I've been trying to figure out an equation for a parabolic line, I've tried all methods I can find around the internet, and several contacts have not been able to assist me.

I need to find the equation that satisfies these three points without giving the letters set numerical values:
(0,C) (T,100) (T+100,100)

Any and All help would be greatly appreciated, it'd been burning my brain to find the answer to this

Let the parabola have the standard form:



From the given points, we have the linear system:



Using this, the system reduces to:





Now you may solve this system to determine in terms of C and T.

You will find then:

This is as far as I was able to get also, however when checking it, the values simply decrease from (0,C) and do not satisfy the points (T,100) or (T+100,100), instead it appears to X intercept at ~70-80% of T, whereas it should pass through 100Y at T and again at T+100

Originally Posted by AtlasSniperman

I need to find the equation that satisfies these three points without giving the letters set numerical values: (0,C) (T,100) (T+100,100)

YES! Thank you so very much MaxJasper, this is exactly what I was looking for, and now that I see both the answer and all the attempts I made I can see how it was done.
Thank you again, it is GREATLY appreciated

That's exactly what I gave you, only in a different form...

I can see the the transition from your form to his, and thank you for helping me see that mark, However when I tried checking your equation it didn't seem to work. I think the difference is "C-" rather than "+C" I'm unsure how but that seems to be the only conversion difference, thank you too for your assistance