1-7 - 1­7 November 18, 2010 1­7 Quadratic functions and...

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Unformatted text preview: 1­7 November 18, 2010 1­7 Quadratic functions and their graphs Quadratic function f(x) = ax2 + bx + c graph is a parabola graph has a vertical axis (x = c) of symmetry . x = c x = ­b/2a vertex Sep 10­9:11 AM if a > 0 open up (vertex is a minimum) if a < 0 opens down (vertex is a maximum) Bigger value of a, narrower the graph .. . . .. . . y = 3x2 y = 2x2 y = x2 Sep 12­9:15 AM 1 1­7 November 18, 2010 given y = ax2 + bx + c c is the y­intercept Roots are the x­intercepts 3 possibilities 1 x­intercept 2 x­intercepts 0 x­intercepts Sep 12­10:34 AM x­intercepts depend on the discriminant x = ­b ± √b2 ­ 4ac 2a This is the discriminant if discriminant is > 0 have 2 x­intercepts if discriminant is = 0 have 1 x­intercepts if discriminant is < 0 have 0 x­intercepts Sep 12­10:37 AM 2 1­7 November 18, 2010 Graphing a quadratic 1. find how it opens, up or down 2. find y ­intercept y = c 3. find x­intercept(s) 4. find axis of symmetry x = ­b/2a 5. find vertex (x,y) 6. graph and label Sep 12­10:47 AM Ex. 1 y = (x + 4)(2x ­ 3) Sep 12­10:49 AM 3 1­7 November 18, 2010 Ex. 2 y = ­2x2 + 12x + 4 Sep 12­10:50 AM H.W. p. 41 1­20 all Sep 12­10:52 AM 4 ...
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This note was uploaded on 04/22/2011 for the course MATH 212 taught by Professor Owens during the Winter '07 term at Grand Valley State University.

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