For any quadratic function, ax2+bx+c, the function, b2- 4ac is called the discriminant.
|Enter any values for a, b and c in the table to the right. Click on the "Evaluate" button and observe the sign of the discriminant.
Then use the sliders below to set the same values of a, b and c on the graph. Observe what happens to the position of the graph. How many times does the curve cross the x-axis?
Change the values and see if your answer is different when b2-4ac is positive, negative and even zero!
- Any quadratic function ax2+ bx + c has discriminant b2-4ac. The quadratic equation ax2+ bx + c = 0 has
- two roots when b2-4ac > 0, and the curve will cross the x axis twice.
- one double root when b2-4ac = 0, and the curve will cross the x axis once.
- no roots when b2-4ac < 0, and the curve will not cross the x axis at all.