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The difference between any perfect square and its predecessor is given by the identity n 2 − (n − 1) 2 = 2n − 1.Equivalently, it is possible to count square numbers by adding together the last square, the last square's root, and the current root, that is, n 2 = (n − 1) 2 + (n − 1) + n.
Figure 1. Plots of quadratic function y = ax 2 + bx + c, varying each coefficient separately while the other coefficients are fixed (at values a = 1, b = 0, c = 0). A quadratic equation whose coefficients are real numbers can have either zero, one, or two distinct real-valued solutions, also called roots.