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Graphing Calculator Activity: Transformations

Graphing Calculator Activity: Transformations Finish investigating the three types of transformations Vertical Translations Dilations Reflections Finish the back of last week’s agenda: HW#11: Transformations Both due at the end of the period today!

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Graphing Calculator Activity: Transformations

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  1. Graphing Calculator Activity: Transformations • Finish investigating the three types of transformations • Vertical Translations • Dilations • Reflections • Finish the back of last week’s agenda: HW#11: Transformations Both due at the end of the period today! See the back of this week’s agenda for examples! Homework: #12: STUDY GUIDE!

  2. Mike graphs the functions y = x2 – 2 and y = 3x2 and on the same set of coordinate axes. State two ways the graphs are different. Explain the reason for each difference Sample Correct Response The graph of y = 3x2 will be narrower than the graph of y = x2 – 2 because the coefficient of 3x2 is larger. The graph of y = x2 – 2 is lower because the -2 shifts the graph down 2 units.

  3. Transformations Conclusions Vertical Translation: • The constant is where the parabola will cross the y-axis. • For example, y = x2 – 8 crosses the y-axis at -8 Dilation: • The higher the value of a, the narrower the parabola • For example, y = 6x2 is narrower than y = x2 • The smaller the value of a, the wider the parabola • For example, y = 1/2x2 is wider than y = x2 Reflection: • If a is negative the parabola is reflected across the x-axis. • For example, y = -x2 + 2 is reflected across the x-axis (upside down u)

  4. A.) The graph is a translation left 2 units from f(x). B.) The graph is a translation right 2 units from f(x). C.) The graph is a translation up 2 units from f(x). D.) The graph is a translation down 2 units from f(x). Describe how the graph of the function g(x) = x2 – 2 is related to the graph of f(x) = x2.

  5. Answer: The graph is stretched horizontally (wider) compared to f(x) = x2 This is the graph of the functiong(x) = 1/2x2. Describe how it is related to the graph of f(x) = x2.

  6. Dave graphs the functions y = 1/4x2 and y = x2 + 2 on the same set of coordinate axes. State two ways the graphs are different. Explain the reason for each difference.

  7. Sample Correct Response The graph of y = 1/4x2 will be wider than the graph of y = x2 + 2 because the coefficient of 1/4x2 is smaller. The graph of y = x2 + 2 is two units higher because the 2 shifts the graph up 2 units. Scoring Guidelines 2: The response provides two ways the graphs are different, along with an adequate explanation of each difference. 1: The response provides evidence of understanding. For example, the response may: • Include only one correct way the graphs are different, with an adequate explanation. • Include two ways the graphs are different, with little or no explanation. 0: Response is incorrect or irrelevant. For example, the response may: • Include only incorrect ways the graphs are different, with no explanation. • Restate the information provided in the item. • Give irrelevant information.

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