# Quadratic Function

Definition: A polynomial? of second degree in one variable is called a quadratic function or quadratic equation.

The general form of a quadratic function is:

\color{red}{ f(x)=ax^2+bx+c}       или       \color{red}{y=ax^2+bx+c}    where    \color{blue}{ a \ne 0} .

Interactivity   Directions for interactivity

Click and drag the slider buttons to change the function.

BTW: Don't be fooled. Changing c does not change the size of the quadratic. It only moves it up and down!

Example:    f(x)=3x^2+2x-1    is a quadratic function    а=3 \quad b=2 \quad c=-1     (other examples?)

 Rules:   The graph of every quadratic function a parabola. The intersection of the parabola with y -axis is unique and is the point (0,с) (see y-intercept). The intersections of the parabola with x -axis (if there is any), are the roots of the function and can be found with the quadratic formula.   The graph shown at right is of the quadratic function: y=x^2-x-6    -->

Related topics:

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Page last modified on November 27, 2008, at 03:48 AM