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Goal: I can infer how the change in parameters transforms the graph. (F-BF.3) Unit 7 Quadratics Translating Graphs

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1. Compare graphs G1, G2 and G3. How have the graphs been affected? 2. Describe the effect of k on the equation f(x) = a(x – h) 2 + k. Changing the 0 to a 2 moved the graph up 2. Changing the 0 to a -3 moved the graph down 3. The k value shifts the graph up and down (vertically).

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It shifts the graph to the left 2 spaces. The h value shifts the graph right and left (horizontally). It shifts the graph to the right 3 spaces.

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It makes the parabola more narrow. The a value widens and narrows the parabola. It makes the parabola wider.

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It made the parabola open down instead of opening up. The a value widens and narrows the parabola and determines the direction it will open. It made the parabola open down instead of opening up AND it made the parabola more narrow.

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Example #1 Describe and graph the transformation of f(x) = x 2 Transformations:Graph: Left 2 spaces Down 3 spaces

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Example #2 Describe and graph the transformation of f(x) = x 2 Transformations:Graph: Opens down Right 1 space Up 4 spaces

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Example #3 Describe and graph the transformation of f(x) = x 2 Transformations:Graph: Opens down Wide Left 2 spaces

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Translating Quadratic Graphs Opens Up/Opens Down Narrow/Wide Moves left or right Moves up or down

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Consider the function: f(x) = 2|x – 2| + 1 1. Does the graph of the function open up or down? 2. Is the graph of the function wider, narrower, or the same.

Consider the function: f(x) = 2|x – 2| + 1 1. Does the graph of the function open up or down? 2. Is the graph of the function wider, narrower, or the same.

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