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f(x) = x 2 f(x) = 2x 2 Parameter ‘a’ increases from 1 to 2 Parabola stretches vertically

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f(x) = x 2 Parameter ‘a’ decreases from 1 to Parabola compresses vertically f(x) = x 2

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f(x) = -x 2 Parameter ‘a’ changes from 1 to -1 Parabola inverts vertically

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f(x) = -x 2 f(x) = -2x 2 Parameter ‘a’ moves from -1 to -2 Parabola stretches vertically

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If f(x) = x 2 and g(x) = ax 2, then the ordered pairs for g(x) can be determined by applying the following adjustment to those from f(x). f(x) = x 2 xf(x) -24 1 00 11 24 xg(x) -28 2 00 12 28 g(x) = 2x 2

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Parameter ‘b’ increases from 1 to 2 Function compresses horizontally

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Parameter ‘b’ decreases from 1 to 0.5 Function stretches horizontally

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Parameter ‘b’ changes from 1 to -1 Parabola inverts horizontally

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Parameter ‘b’ increases from 1 to 2 f(x) = |x| f(x) = |2x| Function compresses horizontally

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Parameter ‘b’ decreases from 1 to ½ f(x) = |x| f(x) = |½x| Function stretches horizontally

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If f(x) = |x| and g(x) = |bx|, then the ordered pairs for g(x) can be determined by applying the following adjustment to those from f(x). Impact of parameter ‘b’ -Horizontal Scale change As ‘b’ moves further from zero, the function compresses horizontally As ‘b’ moves closer to zero, the function stretches horizontally If parameter ‘b’ changes its sign, the graph will invert horizontally f(x) = |x| xf(x) -44 -22 00 22 44 xg(x) -24 2 00 12 24 g(x) = |2x|

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Parameter ‘h’ increases from 0 to 4 Function translates 4 units to the right

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f(x) = |x| f(x) = |x + 2| Parameter ‘h’ decreases from 0 to -2 Function translates 2 units to the left

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Parameter ‘h’ decreases from 0 to -7 Function translates horizontally 7 units to the left

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If f(x) = |x| and g(x) = |x - h|, then the ordered pairs for g(x) can be determined by applying the following adjustment to those from f(x). Impact of parameter ‘h’ -Horizontal Translation As ‘h’ increases from zero, the function translates to the right As ‘h’ decreases from zero, the function translates to the left f(x) = |x| xf(x) -44 -22 00 22 44 xg(x) -64 -42 -20 02 24 g(x) = |x + 2|

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f(x) = x 2 f(x) = x 2 + 2 Parameter ‘k’ increases from 0 to 2 Parabola translates vertically up 2 units

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Parameter ‘k’ decreases from 0 to -7 Function translates vertically 7 units down

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Parameter ‘k’ increases from 0 to 3 Function translates 3 units up

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If f(x) = |x| and g(x) = |x| + k, then the ordered pairs for g(x) can be determined by applying the following adjustment to those from f(x). Impact of parameter ‘k’ -Vertical Translation As ‘k’ increases from zero, the function translates up As ‘k’ decreases from zero, the function translates down f(x) = |x| xf(x) -44 -22 00 22 44 xg(x) -46 -24 -02 24 46 g(x) = |x| + 2

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f(x) = x 2 f(x) = 2(x – 4) 2 - 3 Parameter ‘a’, ‘h’ and ‘k’ all change Parabola stretches vertically, translates to the right and translates down

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Parameter ‘a’, ‘b’ and ‘h’ all change Function stretches vertically, inverts horizontally and translates 3 to the right.

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Impact of parameters ‘a’, ‘b’, ‘h’ and ‘k’ xf(x) 00 11 42 93 xg(x) 34 26 8 -610

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