The discriminant, or b^2-4ac, is part of the quadratic formula that tells us how many solutions a quadratic equation will have (but it doesn't actually tell us what those solutions are.) If the discriminant is greater than zero, you'll have two real solutions; if it is equal to zero, then you'll have one real solution; and if it is less than zero, then you'll have no real solutions. Here we connect the discriminant to basic sketches of functions as well to show how the number of solutions connects to the number of x-intercepts.
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