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1.5 G RAPHING Q UADRATIC F UNCTIONS BY U SING T RANSFORMATIONS

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Graph using the graph of

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You move the key points of To shift to the right 3 spaces you add 3 to all of the x values! xy -24 1 00 11 24 1 2 3 4 5 And then graph the new set of points!

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(1, 4) (2, 1) (3, 0) (4, 1) (5, 4)

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-7 -6 -5 -4 -3 Graph This is a shift to the left 5 spaces. To shift to the left 5 spaces you subtract 5 from all of the x values! xy -24 1 00 11 24 And then graph the new set of points!

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Shift LEFT 5 Units (-7, 4) (-6, 1) (-5, 0) (-4, 1) (-3, 4)

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Graph This is a shift down 4 spaces. To shift down 4 spaces you subtract 4 from all of the y values! 0 -3 -4 -3 0 xy -24 1 00 11 24 And then graph the new set of points!

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Shift DOWN 4 Units (-2, 0) (-1, -3) (0, -4) (1, -3) (2, 0)

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Graph This is a shift up 6 spaces. To shift up 6 spaces you add 6 to all of the y values! 10 7 6 7 xy -24 1 00 11 24 And then graph the new set of points!

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Shift UP 6 Units (-2,10) (-1, 7) (0, 6) (1, 7) (2, 10)

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Graph This is a vertical stretch by a factor of 2. To stretch the parabola you multipy all of the y values by 2 ! 8 2 0 2 8 xy -24 1 00 11 24 And then graph the new set of points!

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Strectch by a factor of 2 (-2,8) (-1, 2) (0, 0) (1, 2) (2, 8)

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Graph This is a vertical compression by a factor of one half. To compress the parabola you multipy all of the y values by 0.5 ! (or divide them all by 2!) 2 0.5 0 2 xy -24 1 00 11 24 And then graph the new set of points!

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Compress by a factor of (-2, 2) (-1, 0.5) (0, 0) (1, 0.5) (2, 2)

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Graph This is a reflection in the x-axis. To reflect the parabola you multipy all of the y values by -1 ! -4 0 -4 xy -24 1 00 11 24 And then graph the new set of points!

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Reflect in the x-axis (-1, -1) (-2, -4) (0, 0) (2, -4) (1, -1)

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Graph -8 -2 0 -8 xy -24 1 00 11 24 reflect in the x-axis and stretch by a factor of 2 shift the parabola up 5 -3 3 5 3 And then graph the new set of points!

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(-1, 3) (-2, -3) (0, 5) (2, -3) (1, 3)

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Graph -9 -8 -7 -6 -5 xy -24 1 00 11 24 shift the parabola left 7 shift the parabola down 3 1 -2 -3 -2 1 And then graph the new set of points!

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(-9, 1) (-8, -2) (-7, -3) (-6, -2) (-5, 1)

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Graph 6 7 8 9 10 xy -24 1 00 11 24 Compress by a factor of 0.25 shift the parabola right 8 1 0.25 0 1 And then graph the new set of points!

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(6, 1) (7, 0.25) (8, 0) (9, 0.25) (10, 1)

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H OMEWORK : P AGE 47 #5 – 12

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