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Unformatted text preview: 14 Quadratic Functions and Their GraphsQuadratic function: has a squared term, but none of higher degreestandard form of the quadratic function:f(x) = ax2+ bx + c(a ≠0)vertex = b2afb2a,vertex form of the quadratic function:f(x) = a(x  h)2+ kvertex = (h, k)parabola: the graph of a quadratic functionThe anatomy of a parabolaThe role of a:if a > 0, parabola opens upwardif a < 0, parabola opens downward14p. 1Finding the vertexExample:f(x) = (x + 1)2 3It is already in vertex form f(x)= (x  h)2+ kso vertex = (h, k) = (1, 3)Example:f(x) = x2+ 2x  2xcoordinate of vertex = b/2a = 2/2 = 1ycoordinate of vertex = f( 1 ) = (1)2+ 2(1) –2 = 3so vertex = (1, 3)Note:this is notthe way shown in the book (i.e. by completing the square), but is far superiorto it14p. 2Sketching the graph of a quadratic functionExample: R(x) = x(2000 – 60x) 1 ≤ x ≤ 25(1) write it in standard form: R(x) = 2000x – 60x2(2) find the vertex: xcoordinate = b/2a = 2000/120 = 50/3 = 16.67xcoordinate = b/2a = 2000/120 = 50/3 = 16....
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This note was uploaded on 12/11/2011 for the course MATH 1324 taught by Professor Staff during the Spring '11 term at Austin Community College.
 Spring '11
 Staff

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