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Ch 6 - Graphing Day 1 - Section 6.1

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Quadratics and Absolute Values parent function: y = x 2 y = a(x - h) 2 + k vertex (h, k) a describes the steepness graph is a parabola (u- shaped) parent function: y = |x| y = a|x - h| + k vertex (h, k) a describes the steepness graph is a v-shape

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Stretching, Shrinking, and Reflecting these properties work with all graph our notes will focus on quadratic and absolute value graphs

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Vertical Stretching when a > 1 function notation: y = a [ f(x) ] verbally: the function is stretched vertically by a factor of a

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Vertical Shrinking when 0 < a < 1 function notation: y = a [ f(x) ] verbally: the function is shrunk vertically by a factor of a

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Vertical Reflection when a < 0 function notation: y = -[ f(x) ] verbally: the function is reflected over they x-axis

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But what happens if the input is multiplied? Let h(x) be represented by the table below. Graph h(x), 2h(x), and h(2x) x-2012 y1-21 1

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Horizontal Shrinking when b > 1 function notation: y = f(bx) verbally: the function is horizontally shrunk by a factor of 1/b.

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Horizontal Stretching when 0 < b < 1 function notation: y = f(bx) verbally: the function is horizontally stretched by a factor of 1/b.

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Summary Vertical Dilations - when the output is multiplied by a constant Reflection over the x- axis when the output is made negative Horizontal Dilations - when the input is multiplied by a constant Reflection over the y-axis when the input is made negative

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Describe how the parent function, p(x) is transformed to h(x) 1. p(x) = x 3 and h(x) = -2x 3 2. p(x) = x 3 + 1 and h(x) = (4x) 3 + 1 3. p(x) = 3x - 2 and h(x) = 15x - 10

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Sketch the graph given the transformations. 1.shrunk vertically by a factor of 2 2.y = -f(x) 3.g(x) = f(x/3)

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