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<?xml version="1.0" encoding="utf-8"?> <!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Strict//EN" "http://www.w3.org/TR/xhtml1/DTD/xhtml1-strict.dtd"> <html xmlns="http://www.w3.org/1999/xhtml"> <head> <title>3.1 - Quadratic Functions</title> <link href=". ./m116.css" rel="stylesheet" type="text/css" /> <meta http-equiv="Content-Type" content="text/html; charset=utf-8" /> </head> <body> <h1>3.1 - Quadratic Functions</h1> <h2>Definitions</h2> <dl> <dt>Polynomial function in one variable of degree n</dt> <dd>A function with one variable raised to whole number powers (the largest being n) and with real coefficients.</dd> <dd>The standard form is f(x) = a<sub>n</sub>x<sup>n</sup> + a<sub>n- 1</sub>x<sup>n-1</sup> + . .. + a<sub>2</sub>x<sup>2</sup> + a<sub>1</sub>x + a<sub>0</sub>, a<sub>n</sub>≠0</dd> <dt>Constant function</dt> <dd>A polynomial function in one variable of degree 0.</dd> <dd>Polynomial form: f(x)=a<sub>0</sub></dd> <dd>Standard form: f(x) = c</dd> <dt>Linear function</dt> <dd>A polynomial function in one variable of degree 1.</dd> <dd>Polynomial form: f(x)= a<sub>1</sub>x + a<sub>0</sub></dd> <dd>Standard form: f(x) = ax + b</dd> <dt>Quadratic function</dt> <dd>A polynomial function in one variable of degree 2.</dd> <dd>Polynomial form: f(x)= a<sub>2</sub>x<sup>2</sup> + a<sub>1</sub>x + a<sub>0</sub></dd> <dd>Standard form 1: f(x) = ax<sup>2</sup> + bx + c</dd> <dd>Standard form 2: f(x) = a (x-h)<sup>2</sup> + k</dd> <dt>Cubic function</dt> <dd>A polynomial function in one variable of degree 3.</dd>

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