A quadratic function have 2 real zeros, 1 real zero, or 2 imaginary zeros. The number of real zeros may be determined by the discriminant. When the discriminant is positive, then you have two real solutions; when is zero, then you have one real solution; and whenever the discriminant is negative, then you don't have real solutions. Explore this interactive applet to view all the described cases. Manipulate any of the sliders to draw a different graph, with different solution set.
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