# Explore the Quadratic Equation

**A Quadratic Equation**

(**a**, **b**, and **c** can have any value, except that **a** can't be 0.)

Try changing a, b and c to see what the graph looks like. Also see the "roots" (the solutions to the equation). Then read more about the Quadratic Equation.

## Explore

Move the a, b and c slider bars to explore the properties of the Quadratic Equation graph.

Look at

- The effect of changes in
**a** - The effect of changes in
**b** - The effect of changes in
**c** - The effect of a negative values of
**a** - The effect of a positive values of
**a** - What happens when
**a=0**? - See if you can get the curve to
**just**touch the x-axis (y=0) - Can you get the "roots" −1.0 and 1.0 ?

## Roots

The "roots" are the solutions to the equation.

When the curve crosses the x-axis (y=0) you will have:

- two solutions
- or ONE solution (if it just touches)

When the curve does **not** cross the line there are still solutions, but:

- the two solutions include
*Imaginary Numbers*