A quadratic function is any polynomial function in one variable that contains a squared term, but has no other term with an exponent greater than 2.
When the graph of quadratic function is plotted, we obtain a parabola (see below)
Note: In the window below, b^2 means b²

y = ax² + bx + c
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Create your own quadratic equation.  Drag the a, b, and c sliders to specify the coefficients of the equation. Drag "1" to change the scale.  Observe the changes on the graph.

1. What happens to the graph when a is negative?
2. The roots of the function is where the graph cuts the x-axis.
   The discriminant, on the other hand, is the name given to the expression (b² - 4ac).
   Click on "discriminant" to observe the relationship between the two.
3. The vertex of a parabola is the highest (or lowest) point of the parabola.  Drag x to find the vertex and observe how it is related to the roots.  Repeat with another graph.