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Graphing Absolute Value Equations

Graphing Absolute Value Equations. Using your graphing calculator graph the parent function: What is the y-intercept? (0, 0) What is the x-intercept? (0,0). Graphing Absolute Value Equations. Keeping the parent graph in the calculator, graph How has the graph changed?

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Graphing Absolute Value Equations

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  1. Graphing Absolute Value Equations Using your graphing calculator graph the parent function: What is the y-intercept? (0, 0) What is the x-intercept? (0,0)

  2. Graphing Absolute Value Equations • Keeping the parent graph in the calculator, graph • How has the graph changed? • It has become steeper when compared to the parent graph. • Have the intercepts changed? • No, the x-intercept and y-intercept are the same as the parent graph.

  3. Graphing Absolute Value Equations • Delete and graph • How has the graphed changed? • It has become flatter when compared to the parent graph. • Have the intercepts changed? • No, the x-intercept and y-intercept are the same as the parent graph.

  4. Graphing Absolute Value Equations • What happens when you multiply the absolute value expression by a given factor . • The graph becomes steeper (or is narrower) when or becomes flatter (or is wider) when • The intercepts of the graph do not change when being compared to the parent graph.

  5. Graphing Absolute Value Equations • What if the value of is negative? • Graph this equation: • What happened? • The graph opened downward instead of upward. • This is called a reflection. • If , there is no reflection • If , there is a reflection

  6. Graphing Absolute Value Equations • Keeping the parent graph in your calculator, enter this equation: • How has the graph changed? • It has shifted horizontally (called a phase shift) two units to the right. • How have the intercepts changed? • The y-intercept has shifted to (0, 2) • The x-intercept has shifted to (2, 0)

  7. Graphing Absolute Value Equations • Delete the previous equation and enter this equation: • How has the graph changed? • It has shifted horizontally (called a phase shift) four units to the left. • How have the intercepts changed? • The y-intercept has shifted to (0, 4) • The x-intercept has shifted to (-4, 0)

  8. Graphing Absolute Value Equations • What happens when you subtract a number inside the absolute value symbol • If , then the graph is shifted horizontally to the right (called a phase shift) • If , then the graph is shifted horizontally to the left (called a phase shift) • The y-intercept changes by the and the x-intercept changes by the given value.

  9. Graphing Absolute Value Equations • Keep the parent graph, delete the previous equation and enter this equation into the calculator: • How has the graphed changed? • The graph has been translated down 1 units (called a vertical shift) • How have the intercepts changed? • The y-intercept has shifted to (0, -1) • There are now 2 x-intercepts (-1, 0) and (1, 0)

  10. Graphing Absolute Value Equations • Delete the previous equation and enter this equation: • How has the graph changed? • The graph has been translated up 3 units (called a vertical shift) • How have the intercepts changed? • The y-intercept has shifted to (0, 3) • There are no x-intercepts

  11. Graphing Absolute Value Equations • How does adding or subtracting a number outside the absolute value symbol affect the graph • If , the graph is translated up (called a vertical shift) • If , the graph is translated down (called a vertical shift)

  12. Graphing Absolute Value Equations • Can the graph of an absolute value equation that has been translated up have x-intercepts? • Yes, when the value of . • Try this example:

  13. Comparing to the parent graph • Graph at the same time on your calculator. • What comparison can be made? • The graph is 3 times steeper, has a phase shift two units to the right with no vertical shift or reflection when compared to the parent graph.

  14. Comparing to the parent graph • Graph at the same time on your calculator. • What comparisons can be made? • The graph has been reflected and opens wider with a phase shift of 3 units to the left and a vertical shift down 2 units when compared to the parent graph.

  15. Homework Assignment Page 397 1- 7 all. Graph the parent equation along with the equation given in the problem at the same time on your calculator. Then write comparison statements like those on the previous two slides.

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