The Discriminant
For any quadratic function, ax^{2}+bx+c, the function, b^{2} 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 xaxis? Change the values and see if your answer is different when b^{2}4ac is positive, negative and even zero! 
Summary
 Any quadratic function ax^{2}+ bx + c has discriminant b^{2}4ac. The quadratic equation ax^{2}+ bx + c = 0 has
 two roots when b^{2}4ac > 0, and the curve will cross the x axis twice.
 one double root when b^{2}4ac = 0, and the curve will cross the x axis once.
 no roots when b^{2}4ac < 0, and the curve will not cross the x axis at all.