How can I calculate a polynomial trend line where `y` always increases as `x` increases?

Question

Assume the following given coordinates: [0,0],[12,200],[24,2000].

The following equation generates a second order polynomial trend line (at least that's what excel tells me) :

y = 800x^2 - 2200x + 1400

However, between 0 and 12 on the x axis, the y values are negative.

How can I calculate a trend line where the values of y always increase as x increases?

Answer 1

If your trend line must go through those points, then you're probably stuck. If you just want a "trend line" that gives the "general trend", then plot a literal line. That is, tell Excel to give you a linear fit, $y=mx+b$, no quadratic term.