Quadratic Function

Definition: A polynomial ? of first 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 -->