Using three points to create a quadratic equation produces an equation, which doesn't seem to pass through the original points

Question

I've got three (x,y) points from which I am trying to create a quadratic equation, which are:

(2325, 5500)
(1880, 3700)
(1400, 2360)

Using those three points, I create three simultaneous equations:

5500 = 5405625a + 2325b + c
3700 = 3534400a + 1880b + c
2300 = 1960000a + 1400b + c

From there, this is the quadratic equation I produce:

y = 0.0014x^2 - 1.6524x + 2017.7

This seems to be the right equation. In addition, when I generate the equation through Excel and online tools, the same one results. However, when I input the x-values from my original three points, they're all out quite significantly. Compared to the original points, these are the points (using the same x-values) that the equation produces:

(2325, 5744)
(1880, 3859)
(1400, 2448)

There must be something I have done wrong (and most likely something quite basic) but shouldn't the equation I create from the three points give the correct y-values when I use the same x-values? Can someone please point out to me what is going wrong, and how I can fix it? Thanks!

Answer 1

You're simply using too few significant digits in the most important part, the coefficient $a$:

I have it as $0.0013548942$ to 8sf on an online solver. Note that the error to $0.0014$ is a full $3.3\%$, which is enough to see the deviations in your crosscheck.

Answer 2

As long as you can, use whole numbers up to the end.

This would give $$\left\{a= \frac{2677}{1975800},b= -\frac{652957}{395160},c= \frac{6644445}{3293}\right\}$$