I have calculated four approximate points from a sensors to get information. I would like to deduce the closest parabola to my points. The problem is that I can't solve it to get an appropriate result.
Here are my four points: $(414, 960), (1020,2340), (1387,3300), (1848,4510)$
Also, I tried to solve it with Wolfram Alpha using this instruction: solve $ \begin{align*} 171396a+397440b+921600c+414d+960e+f&=0\\ 1040400a+2386800b+5475600c+1020d+2340e+f&=0\\ 1923769a+4577100b+10890000c+1387d+3300e+f&=0\\ 3415104a+8334480b+20340100c+1848d+4510e+f&=0\\ b^2=4ac \end{align*} $
I wasn't able to make it works... I might not have the correct syntax. Any help will be appreciate.