An expression of the form ax^{2} + bx + c is called a quadratic expression. The value of this expression is usually plotted on the Cartesian plane along y axis. Then the expression is denoted as y = ax^{2} + bx + c. Let us find when the expression is positive, negative and zero. As the expression is a combination of a variable and three constants and is a simple addition of three terms and does not take the form 0/0, 0^{0}, ∞/∞ , ∞−∞ , 0×∞ , 1^{∞} and ∞^{0} for any value of x, the function y = ax^{2} + bx + c is continuous and takes every value in the range −∞ to +∞ for −∞<x<+∞. By the factor theorem we can express the expression y = ax^{2} + bx + c as the product of two terms because if the value of y is 0 for some value α then (x − α) is a factor the the expression. On finding one such factor the other factor can be found vary easily. Suppose we have found two factors (x − α) and (x − β) such that α<β. Then y = a(x − α)(x − β). The expression is positive, negative or zero according to the expression containing factors if a>0.

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