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!

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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