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Understanding Non-linear Functions: Quadratics and Rational Functions

This session focuses on key concepts in non-linear functions, particularly quadratics and rational functions, funded by the Arizona Board of Regents' Improving Teacher Quality initiative. Participants will learn how to graph equations, solve quadratic equations using factoring and the quadratic formula, and identify solution sets for inequalities. The session includes practical examples and real-world applications, such as modeling growth and changes in temperature. Participants will apply their knowledge by analyzing student errors in problem-solving and determining asymptotes in graphing rational functions.

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Understanding Non-linear Functions: Quadratics and Rational Functions

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  1. Session 4 Project: IMPAQ Non-linear Functions Funded in part by the Arizona Board of Regents, Improving Teacher Quality

  2. Which of the following represents the graph of the equation ?

  3. Solve Quadratic EquationsFactor or Quadratic Formula Factor

  4. Quadratic Formula

  5. Solve the following quadratic:

  6. Use the problem and solution below to answer the question that follows. • A student performed the • steps to solve the problem. • In which step did the • student introduce an • error? • step 1 • step 2 • step 3 • step 4

  7. Which are the solutions to this equation? • x = -3 or x = -4 • x = 3 or x = 4 • x = -1 or x = -4 • x = 4 or x = -3 • x = 4 or x = 1

  8. Which of the following represents the solution set for the system of inequalities:

  9. Rational Functions Graph Determine asymptotes Vertical Asymptote: x – 2 = 0 Horizontal Asymptote: Plot two points to the left and right of the vertical asymptote

  10. Determine the vertical and horizontal asymptotes of the graph of the function.

  11. Graph

  12. Graph

  13. Graph

  14. Which of the following real-world situations could best be modeled by the following graph? • The height of a person growing from child to adult. • The temperature of a cake after it is taken out of the oven. • The height of an airplane landing on a runway. • The amount of gasoline in a car gas tank during a long trip.

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