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**1.6 Using Multiple Transformations to graph quadratic equations**

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When graphing a quadratic function we can apply the transformations to the key points of But after yesterday maybe you noticed that the vertex is easy to move left or right and never gets effected by the stretch or compression factor. Always stretch or compress the parabola first!

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-10 -5 5 10 15 -15 X Y 5 3 1 The “STEP PATTERN” of is “1, 3, 5” and it is the step pattern that changes when the parabola is stretched or compressed!

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**Graph This is a vertical stretch by a factor of 3 so we multiply the step pattern by 3 **

1 , 3 , 5 x3 3 , 9 , 15

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-10 -5 5 10 15 -15 X Y 15 9 3

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**X-2 Graph reflect in the x-axis stretch by a factor of 2**

shift the parabola right 5 shift the parabola up 3 We can graph it by moving the vertex right 5 and up 3 and using the step pattern to draw the other key points 1 , 3 , 5 X-2 -2 , -6 , -10

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-10 -5 5 10 15 -15 X Y -2 -6 -10

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Graph stretch by a factor of 3 shift the parabola left 1 shift the parabola down 7

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-10 -5 5 10 15 -15 X Y

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Graph reflect in the x-axis compress by a factor of 0.5 shift the parabola right 8 shift the parabola up 6

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-10 -5 5 10 15 -15 X Y

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Graph reflect in the x-axis stretch by a factor of 2 shift the parabola left 4 shift the parabola up 5

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-10 -5 5 10 15 -15 X Y

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Graph compress by a factor of shift the parabola right 2 shift the parabola down 5

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-10 -5 5 10 15 -15 X Y

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Homework: Page 56 #1 – 11

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