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Published byKaylee Todd Modified over 2 years ago

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Graphical Transformations Vertical and Horizontal Translations Vertical and Horizontal Stretches and Shrinks

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Take the equation f(x)= x 2 How do you modify the equation to translate the graph of this equation 5 units to the right? units to the left? How do you modify the equation to translate the graph of this equation 3 units down? units up? What if you wanted to translate the graph of this equation 5 units to the left and 3 units down?

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The parabola has been translated 5 units to the right. How is the equation modified to cause this translation?

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Notice the change in the equation y = x 2 to create the horizontal shift of 5 units to the right. f(x) = x 2 g(x) = (x-5) 2

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The parabola is now translated 5 units to the left. How is the equation modified to cause this translation?

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Notice the change in the graph of the equation y=x 2 to create a horizontal shift of 5 units to the left. h(x)=(x+5) 2 f(x)=x 2

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The parabola has now been translated three units down. How is the equation modified to cause this translation?

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q(x)=x 2 -3 f(x)=x 2 Notice how the equation y = x 2 has changed to make the Vertical translation of 3 units down.

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The parabola has now been translated 3 units up. How is the equation modified to cause this translation?

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Notice how the equation y = x 2 has been changed to make the Vertical translation 3 units up. f(x)=x 2 r(x)=x 2 +3

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Write what you think would be the equation for translating the parabola 5 units to the left and 3 units up?

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The equation would be What would the graph would look like?

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g(x) is the translation of f(x) 5 units to the left and 3 units up. f(x)= x 2 g(x) = (x+5) 2 +3

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Vertical and horizontal stretches and shrinks How does the coefficient on the x 2 term affect the graph of f(x) = x 2 ? What if we substitute an expression such as 2x into f(x)? How would that affect the graph of f(x) = x 2?

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The parabola has been vertically stretched by a factor of 2. Notice how the equation has been modified to cause this stretch.

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The parabola is vertically shrunk by a factor of ½. Notice how the equation has been modified to cause this shrink.

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By substituting an expression like 2x in for x in f(x) = x 2 gives a different type of shrink. f(2x) = (2x) 2. A horizontal shrink by a factor of ½.

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Suppose we found g(1/2x). The equation would be y = (1/2x) 2.. How would this affect the graph of the function g(x) = x 2 ? It is a horizontal stretch by a factor of 2.

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If we were to write some rules for translations of functions and stretches/shrinks of functions, what would we write? Horizontal translation: Vertical translation: Vertical stretch: Vertical shrink: Horizontal stretch: Horizontal shrink:

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