## The Discriminant

For any quadratic function, ax2+bx+c, the function, b2- 4ac is called the discriminant.

For example:
• x2+4x+1 has discriminant 16 - 4 = 12
• x2+6x+9 has discriminant 36 - 36 = 0
• x2+x+3 has discriminant 1 - 12 = -11
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!
 a = b = c = b2- 4ac

### Summary

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.