Quadratic
A parabola. Use it for height against time in free fall or projectile motion, and for calibration curves with slight, steady curvature.
Fit the example dataStart with your own data
Example: NIST’s Pontius load cell calibration data, 40 points with y uncertainties, opened as a new copy you can edit.
Parameters
- Coefficient of x²: half the curve’s second derivative.
- Coefficient of x: the slope at x = 0.
- Value of y at x = 0.
Tips
- For height against time in free fall, a = −g/2, b is the initial vertical velocity and c the initial height.
- Use the lowest degree that leaves no pattern in the residuals. AIC in Fit Statistics penalizes each extra coefficient, and Previous compares fits of the same data.
- With no uncertainties selected, the goodness of fit is R², because the model is linear in its parameters.
- For a calibration curve, Evaluate’s y → x reads x from a measured y within the fitted range, and lists both solutions where a parabola gives two.