3_1 - one x-intercept = the vertex ( TOUCH ). b 2-4 ac...

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Section 3.1: Quadratic Functions and Models Instructor: Ms. Hoa Nguyen (nguyen@scs.fsu.edu) 1 Graphs Quadratic function ( a 6 = 0): f ( x ) = ax 2 + bx + c (1) a > 0: parabola opens UP . a < 0: parabola opens DOWN . Figure 1: a > 0 Figure 2: a < 0 If h = - b 2 a and k = f ( h ), then f ( x ) = ax 2 + bx + c = a ( x - h ) 2 + k (2) Vertex : ( h, k ) = ( - b 2 a , f ( - b 2 a )). a > 0: vertex is the MINIMUM point. a < 0: vertex is the MAXIMUM point. Axis of symmetry : the line x = - b 2 a . 1
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Example 1 Example 2 2 The x -Intercepts: the points where the graph will cross or touch the x -axis. The discriminant: b 2 - 4 ac . b 2 - 4 ac > 0: two distinct x -intercepts ( CROSS ). b 2 - 4 ac = 0:
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Unformatted text preview: one x-intercept = the vertex ( TOUCH ). b 2-4 ac &lt; 0: zero x-intercept ( NOT CROSS NOR TOUCH). Example 3 2 Example 4 Rules to select the RIGHT graph of the quadratic function: f ( x ) = ax 2 + bx + c Check the sign of a to see if the parabola is open up or down. Compute the vertex (-b 2 a , f (-b 2 a )). If the above steps are not enough to identify the graph, check the x-intercepts. Example 5 3 Example 6 Example 7 4...
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3_1 - one x-intercept = the vertex ( TOUCH ). b 2-4 ac...

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