## Linear Function

Consider a function of the form y = a_{1}x + a_{0} where a_{1} ≠ 0.

### Two Points

If two distinct points (x_{1},y_{1}) and (x_{2},y_{2}) are known and x_{1} ≠ x_{2}, then the coefficients are given by

### One Point and a Slope (Gradient)

If one point (x_{1},y_{1}) is known, along with the slope (gradient) m, then the coefficients are given by

## Quadratic Function

Consider a function of the form y = a_{2}x^{2} + a_{1}x + a_{0} where a_{2} ≠ 0.

### Three Points

If three distinct points (x_{1},y_{1}), (x_{2},y_{2}) and (x_{3},y_{3}) are known and x_{1} ≠ x_{2} ≠ x_{3} ≠ x_{1}, then the coefficients are given by

### Two Points and a Slope (Gradient)

If two distinct points (x_{1},y_{1}) and (x_{2},y_{2}) are known with x_{1} ≠ x_{2}, along with the slope z_{3} at x = x_{3} with x_{3} ≠ (x_{1} + x_{2})/2, then the coefficients are given by

### One Point and Two Slopes (Gradients)

If one point (x_{1},y_{1}) is known, along with the slopes z_{2} at x = x_{2} and z_{3} at x = x_{3} (x_{2} ≠ x_{3}), then the coefficients are given by