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Unit 1: Function Families Lesson 5: Transformations & Symmetry Notes 2.11- Graph y = ax 2 + bx + c

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The graph of a Quadratic Function (y = ax 2 + bx + c) Parabola: Opens ______ if a > 0. Opens ______ if a < 0. Is __________ than y = ax 2 if | a | > 1. Is __________ than y = ax 2 if | a | < 1. Minimum/Maximum: Has _________ if a > 0. Has _________ if a < 0.

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The graph of a Quadratic Function (y = ax 2 + bx + c) Axis of symmetry: The line that passes through the vertex and divides the parabola into 2 symmetric parts. x = ____ Vertex: (____, ____) Use axis of symmetry as x-value. Substitue into function to find y-value.

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(Ex 1) Find the axis of symmetry and the vertex. Consider the function y = -2x 2 + 16x – 15. a) Find the axis of symmetry of the graph of the function.

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(Ex 1) Find the axis of symmetry and the vertex. Consider the function y = -2x 2 + 16x – 15. b) Find the vertex of the graph of the function. Is this vertex a max or min?

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Checkpoint: Find the axis of symmetry and the vertex of the graph of the function. Determine if the vertex is a max or min. 1. y = 3x 2 + 18x + 5 2. y = ¼ x 2 – 4x + 7

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(Ex 2) Graph y = ax 2 + bx + c Graph y = -x 2 + 4x – 1. Step 1: Determine whether the parabola opens up or down. Step 2: Find and draw the axis of symmetry. x = -b 2a

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(Ex 2) Graph y = ax 2 + bx + c Graph y = -x 2 + 4x – 1. Step 3: Find and plot the vertex. Step 4: Find and plot 2 points on 1 side.

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(Ex 2) Graph y = ax 2 + bx + c Graph y = -x 2 + 4x – 1. Step 1: Down Step 2: x = 2 Step 3: (2, 3) Step 4: (1, 2), (0, -1) Step 5: Reflect those points on other side. Step 6: Draw parabola.

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Checkpoint: Graph the function. Label the vertex and axis of symmetry. 3. Graph y = 4x 2 + 8x + 3. Step 1: Step 2: Step 3: Step 4: Step 5: Reflect points. Step 6: Draw parabola.

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(Ex 3) Compare Graphs. Compare the graph of f(x) = x 2 – 8x + 16 and g(x) = -x 2 + 8x – 16.

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Checkpoint: Compare the graphs of f(x) and g(x). 4. f(x) = x 2 + 6x + 5 g(x) = x 2 – 6x + 5

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Checkpoint: Compare the graphs of f(x) and g(x). 4. f(x) = x 2 + 3x + 4 g(x) = -x 2 – 3x – 4

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Assignment p. 107 # 23-26 (all); 36-38 (all)

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