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Unformatted text preview: Math 1650 Lecture Notes 2.5 Jason Snyder, PhD. Quadratic Functions; Maxima and Minima Page 1 of 6 2.5: Quadratic Functions; maxima and Minima Graphing Quadratic Functions Using the Standard Form A quadratic function is a function of the form = ? 2 + ? + ? where ? , ? , and ? are real numbers and ? . For example, if we take ? = 1, ? = ? = 0 , we get the simple quadratic function = 2 . The graph of any quadratic function is called a parabola , and can be obtained from the graph of = 2 by the transformations discussed in 2.4. Example 1 Standard Form of a Quadratic Function Let = 3 2 12 + 20. (a) Express in standard form. (b) Sketch the graph of . = ? 2 + Standard Form of a Quadratic Function A quadratic function = ? 2 + ? + ? can be expressed in the standard form by completing the square. The graph of is a parabola with vertex (h,k); the parabola opens upward if ? &gt; 0 or downward if ? &lt; 0 . Math 1650 Lecture Notes...
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- Spring '06
- Math, Jason Snyder