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4. Process Modeling
4.8. Some Useful Functions for Process Modeling
4.8.1. Univariate Functions
4.8.1.1. Polynomial Functions

4.8.1.1.2.

Quadratic Polynomial

example of quadratic polynomials
Function:  
f(x) = \beta_0 + \beta_1x + \beta_2x^2, \ \ \beta_2 \neq 0
Function
Family:

Polynomial
Statistical
Type:

Linear
Domain:  

(-\infty, \ \infty)
Range:  
\left\{
\begin{array}{ll}
\left.(-\infty, \ \beta_0-\frac{\beta_1^2}{4\beta_2}\right.] & \mbox{for $\beta_2 < 0$} \\
 & \\
\left.[\beta_0-\frac{\beta_1^2}{4\beta_2}, \ \infty\right.) & \mbox{for $\beta_2 > 0$}
\end{array}
\right.
Special
Features:

None
Additional
Examples:
quadratic polynomial example 1: y = -2*(x+2)(x-7); 2 < x < 3
quadratic polynomial example 2: y = x**2 + 132; -10 < x < 0
quadratic polynomial example 3: y = -2*(x+2)(x-7), 6 < x < 10
quadratic polynomial example 4: y=x**2 + 132; 10 < x < 30
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