To illustrate both the importance of notation and the function concept, we could consider one of the classic problems in algebra, solution of the quadratic equation. In modern notation such an equation would be written Ax2 + Bx + C = 0. Here it is understood that A, B, and C represent numbers, x represents the unknown quantity to be found, and the small 2 appearing in the first term means that the unknown x is to be squared or multiplied by itself. While the solutions to some forms of this equation were known to the ancient Babylonians, the notation was not fully developed until the work of the French mathematician François Viète (1540-1602), who standardized the use of letters to represent both constants and variable quantities. Given this notation, it is then an easy thing to think about the equation as having the form f(x) = 0. Where the function f(x) = Ax2 + Bx + C. One can then think of a second variable, say y, being defined by the function, y = f(x) = Ax2 + Bx + C, so that we have a relation between the two variables x and y that can be studied in itself.
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