Quadratic Functions, Translation and Reflection

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Quadratic Functions,Translation and Reflection

• Lesson 2.2

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Quadratic Function

• Standard form
• a, b, and c are constants
• a ? 0 (why?)
• Vertex form
• (h, k) is the vertex of the parabola
• value for a is the same in both forms

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Vertex of Parabola

• X-value of vertex at
• Y-value of vertex at
• For

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Translations

• In the Y screen, enter the function
• Now enter the variations as shown
• Predict the results of the variations

• Set style
• dotted
• thick

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Horizontal Translations

• Shift to the right f(x a)
• Shift to the left f(x a)

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Translations

• Now try make predictions
• These changescreated verticaltranslations
• f(x) a shift up
• f(x) a shift down

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Translations

• What about? Predictions?
• When a gt 1gives verticalstretch
• When 0 lt a lt 1gives vertical compression

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Reflections

• Make your predictions again for these variations
• -f(x) gives reflectionin the x-axis
• f(-x) gives reflectionin y-axis

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Combinations

• Given
• What happens when we have these variations?

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Assignment

• Lesson 2.2
• Page 79
• Exercises 1 61 EOO