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Class_Notes_3.3

# Class_Notes_3.3 - 29 29 29 29 2 2 2 3 2 4 a f x x x b f x x...

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Mini-Lecture 3.3 Quadratic Functions and Their Properties Framing Thoughts for this Section We’ve already drawn graphs of parabolas in chapter 2, but there we did it by plotting points. Here we re-examine parabolas (that represent functions) using the language and notation of functions. We look at how every quadratic function’s graph can be found by transforming the basic quadratic function 2 ( ) = f x x . In addition, we will think about how some of the general properties of functions we studied in chapter 2 apply to quadratic functions. Guiding Question 1 Graph each function by using transformations on the function ( 29 2 f x x = . ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 2 2 2 2 2 3 1 3 a f x x b f x x = - - = - + + Guiding Question 2 Find the vertex, axis of symmetry, intercepts and graph the function. State the domain and range, and where the function is increasing and where it is decreasing.

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Unformatted text preview: ( 29 ( 29 ( 29 ( 29 2 2 2 3 2 4 a f x x x b f x x x =--= --Guiding Question 3 Determine the value of the maximum or the minimum without graphing. ( 29 ( 29 ( 29 ( 29 2 2 3 24 53 2 12 24 a f x x x b f x x x =-+ = ---Answers: 1.(a) Move 2 right, down 2, stretch of 2 (b) Reflect, 1 left, up 3, stretch of 3 2. (a) Vertex = (3/4,-25/8); Axis of symmetry: x=3/4; x-intercepts -1/2, 2; y-intercept = -2 Domain = ( 29 ,-, Range = [ 29 25/8,-, Decreasing ( 29 ,3/ 4-, Increasing ( 29 3/ 4,e (b) Vertex = (-2,4); Axis of symmetry: x=-2; x-intercepts -4, 0; y-intercept = 0 Domain = ( 29 ,-, Range = ( ] ,4-, Increasing ( 29 , 2--, Decreasing ( 29 2,-(a) (b) 3. (a) Minimum is 5 (b) Maximum is -6...
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Class_Notes_3.3 - 29 29 29 29 2 2 2 3 2 4 a f x x x b f x x...

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