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Teacher Notes

Teacher Notes. Copies: Quadratic Function G.O. (I, II, III) Hour #1—go to graphing f(x) = ax 2 +c homework —worksheet Hour #2—go to average rate of change, homework —worksheet and add this family of functions to the scrapbook

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Teacher Notes

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  1. Teacher Notes • Copies: Quadratic Function G.O. (I, II, III) • Hour #1—go to graphing f(x) = ax2+c homework—worksheet • Hour #2—go to average rate of change, homework—worksheet and add this family of functions to the scrapbook • Hour #3—Complete through tasks #1, 2, and 4 homework—complete #3 and review work

  2. Quadratic Functions Unit 1 Lesson 4

  3. It’s a curved world… • Let’s look at some photos. • Each photo has some type of curve in it. Using a colored pencil, trace the curve(s) in each picture. • Which curve(s) appear to be symmetrical?

  4. What is a quadratic function? • A quadratic function is a nonlinear function that can be written as f(x) = ax2 + bx + c where a ≠ zero. • Basic quadratic function in this family of functions is called the parent quadratic function f(x) = x2

  5. Every quadratic function has a U-shaped graph called a parabola. The lowest or highest point on the parabola is the vertex. The line that divides the parabola into two symmetric parts is called the axis of symmetry. Axis of symmetry Vertex Graph of a Quadratic Function

  6. Exploring Quadratic Functions • With your partner, complete the table, graph your results, and answer the questions. • You have 10 minutes!

  7. Parent function f(x) = x2 Complete the graphic organizer for f(x) = x2 (Quadratic Functions Graphic Organizer I) With your partner, compare your graphs and answers to the questions. Find each of the terms from the last slide for this and each of the graphs that follow!

  8. That’s a Good Point! When choosing points to use for graphing the parent function of quadratic equations, follow these easy steps: • Always choose zero as the x-coordinate as one of your points • For the other coordinates, when you choose a positive number for x, choose the same negative number! Why? • Choose at least 5 sets of points to graph

  9. Coefficients… how do they affect my graph? • Complete the graphic organizer titled “Quadratic Functions Graphic Organizer II” on the function f(x) = ax2 • With your partner, compare your paper and graphing calculator results. • Remember to find the domain, range, etc. • Be prepared to share your findings with the class!

  10. f(x) = ax2 + c • Complete the graphic organizer for f(x)= ax2 + c (Quadratic Functions Graphic Organizer III) • Graph the equations on the calculator when you are finished with the graphic organizer. • Predict what will happen if the 3 is replaced with a 5. What about if it becomes a 1?

  11. Transformation practice • With your partner, complete the Exploring Quadratic Functions—Transformations worksheet. • You may use the graphing calculator or graph the functions on paper to answer the questions.

  12. Average Rate of Change • Slope of the line between any two points • Use two points (x1, f(x)1) and (x2, f(x)2) • Formula: f(x)2 – f(x)1 x2 – x1 Example: Find the average rate of change in f(x) = x2 – 3 when x1 = 0 and x2 = -2 **Teacher led example

  13. Your turn! Find the average rates of change for the following: • f(x) = x3 -1 when x1 = -2 and x2 = 0 • f(x) = ½ x2 when x1 = 0 and x2 = 2 • f(x) = -3x + 15 when x1 = 0 and x2 = 2

  14. Round the Room Review • 10 volunteers to participate at a time. • Number your paper 1-10 • If you end up at the station where you started, you have made an error. You MUST retrace your steps to find it! • Once you are finished with the review, turn your paper in. • The rest of the class should be working on review work.

  15. Walking, Falling, and Making Money Task • Complete #1, 2, and 4 with your partner. • Be prepared to share your findings with the class! • If you get finished before the rest of the class, you may start your homework (#3)

  16. Summary • Standard form: f(x) = ax² + bx + c, where a≠0, a,b,and c are real numbers, and c is the y-intercept. • Characteristics: Has a vertex (min or max), U shape…called a parabola • Domain: All Real Numbers • Range: (0, ∞) when a is positive (0, -∞) when a is negative.

  17. Act It Out  • With your partner, act out the transformations from the parent function. • One partner is the function, the other partner moves his/her hands where they should be when I announce what transformation I am looking for.

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