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 below to see how they change the curve. Notice the roots (the solutions to the equation, shown as dots on the graph).

Read more about the Quadratic Equation.

Explore

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

Look at:

• The Curve Direction: What makes the curve open upward like a smile, or downward?
• What does "b" do? Can you figure it out?
• The "c" Effect: What happens to the curve when you change only c?
• The Zero Trap: What happens to the curve when a = 0 ?
• The Perfect Touch: Can you adjust the sliders so the curve just touches the x-axis at exactly one point?
• Target Practice: Can you find values for a, b, and c that make the roots exactly −1.0 and 1.0?

Roots

The roots are the solutions to the equation.

When the curve crosses the x-axis (y=0) we 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