Your code for calculating the residuals for the quadratic regression contains this line:
fit_line = x*a0**2 + x*a1 + a2
Which leads to the output that the sum of residuals is -584
In fact, the line should be
fit_line = a0*x**2 + x*a1 + a2
as the coefficient is for the x^2 term, not the root of the coefficient for the x term
When corrected, this gives the output that the sum of the residuals is actually 1.4139800441625994e-12, which is actually much smaller than the residual for the linear fit!
This entirely invalidates the paragraph which follows it, which explains why the number is so large.