4.8.1.1.2. Quadratic Polynomial


Function:	$ \displaystyle f(x) = \beta_0 + \beta_1x + \beta_2x^2, \ \ \beta_2 \neq 0$
Function Family:	Polynomial
Statistical Type:	Linear
Domain:	$ \displaystyle (-\infty, \ \infty) $
Range:	$ \displaystyle \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:


Function:	\( \displaystyle f(x) = \beta_0 + \beta_1x + \beta_2x^2, \ \ \beta_2 \neq 0\)
Function Family:	Polynomial
Statistical Type:	Linear
Domain:	\( \displaystyle (-\infty, \ \infty) \)
Range:	\( \displaystyle \left\{ \begin{array}{ll} \left(-\infty, \ \beta_0-\frac{\beta_1^2}{4\beta_2}\right] & \mbox{for $\beta_2 < 0$} \\ & \\ \left[\beta_0-\frac{\beta_1^2}{4\beta_2}, \ \infty\right) & \mbox{for $\beta_2 > 0$} \end{array} \right. \)
Special Features:	None
Additional Examples: