Do Now: Think about what you learned from Chapter 1. How do you think the constants a, h, and k affect the graph of the quadratic function y = a(x.

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Presentation transcript:

Do Now: Think about what you learned from Chapter 1. How do you think the constants a, h, and k affect the graph of the quadratic function y = a(x − h)2 + k?

2.1: Transformationof Quadratic Functions

Quadratic Function: y = a(x - h)2 + k Vertex: (h, k) Parabolic shape (u-shaped) If a is positive, the parabola will open up, if a is negative it will open down. Vertical line of symmetry: x = h

Transformations of Quadratic Functions Vertex: (h, k) Tells if graph opens up (+) down (-) Reflection Stretch or shrink Take opposite value Moves left (+) Moves right (-) Tells movement Up (+) Down (-)

Different Stretches and Shrinks

Example: x y Opening: up or down? Left/right transformation: Stretch/Shrink: Up/down transformation:

Example: g(x) = 2(x)2 + 1 x y Opening: up or down? Left/right transformation: Stretch/Shrink: Up/down transformation:

Example: x y Opening: up or down? Left/right transformation: Stretch/Shrink: Up/down transformation:

Practice x y Opening: up or down? Left/right transformation: 1. Describe the transformation of f (x) = x2 represented by g. Then graph the function. g(x) = (x + 4) 2 − 1. x y Opening: up or down? Left/right transformation: Stretch/Shrink: Up/down transformation:

Practice g(x) = (x − 3) 2 x y Opening: up or down? 2. Describe the transformation of f (x) = x2 represented by g. Then graph the function. g(x) = (x − 3) 2 x y Opening: up or down? Left/right transformation: Stretch/Shrink: Up/down transformation:

Practice g(x) = (x − 2) 2 − 2 x y Opening: up or down? 3. Describe the transformation of f (x) = x2 represented by g. Then graph the function. g(x) = (x − 2) 2 − 2 x y Opening: up or down? Left/right transformation: Stretch/Shrink: Up/down transformation:

Practice g(x) = (x + 5) 2 + 1 x y Opening: up or down? 4. Describe the transformation of f (x) = x2 represented by g. Then graph the function. g(x) = (x + 5) 2 + 1 x y Opening: up or down? Left/right transformation: Stretch/Shrink: Up/down transformation:

Practice 5. Describe the transformation of f (x) = x2 represented by g. Then graph the function. x y Opening: up or down? Left/right transformation: Stretch/Shrink: Up/down transformation:

Match each quadratic function with its graph. Explain your reasoning Match each quadratic function with its graph. Explain your reasoning. Then use a graphing calculator to verify that your answer is correct. 1. y = −(x − 2)2 2. y = (x − 2)2 + 2 3. y = −(x + 2)2 − 2 4. y = 0.5(x − 2)2 − 2 5. y = 2(x − 2)2 6. y = −(x + 2)2 + 2

Homework p52, #8, 10, 20, 22, 24 * You will need graph paper

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Practice: Match each function with its graph.

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