1-4 - 1-4 Quadratic Functions and Their GraphsQuadratic...

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Unformatted text preview: 1-4 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 downward1-4p. 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 - 2x-coordinate of vertex = -b/2a = -2/2 = -1y-coordinate 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 it1-4p. 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: x-coordinate = -b/2a = -2000/-120 = 50/3 = 16.67x-coordinate = -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.

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1-4 - 1-4 Quadratic Functions and Their GraphsQuadratic...

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