[The following questions were adapted from Polygraph: Parabolas, Part 2]

Transcription

1 Opening Exploration 1. Go to and use the class code: to play Polygraph: Parabolas. A description of the game is given below. [The following questions were adapted from Polygraph: Parabolas, Part 2] 2. During Polygraph: Parabolas, Edwin asked this question: Is your parabola s turning point below the x-axis? What other word or phrase could we use for turning point? 3. During Polygraph: Parabolas, Sarah asked this question: "Does your parabola look like a smile?" Sketch a parabola that might look like a smile to Sarah on the grid to the right. Instead of saying "looks like a smile," mathematicians say CONCAVE UP. Likewise, instead of "looks like a frown," mathematicians say CONCAVE DOWN. 4. Sketch a concave down parabola with vertex (4, -2) on the same grid. Unit 8: Introduction to Quadratics & Their Transformations S.29

2 5. During Polygraph: Parabolas, Mia asked this question: "Does your parabola touch the middle line twice?" A. Why is this question potentially ambiguous? B. What other word or phrase could we use for "touches the middle line twice"? 6. During Polygraph: Parabolas, Miguel asked this question: "Does the y-axis cut the parabola in half?" What other word or phrase could we use for "cut the parabola in half"? 7. Which of these statements are true for the parabola shown here? Select all that apply. Vertex on the y-axis. Concave down. One positive x-intercept. One negative y-intercept. Line of symmetry at y = Sketch a parabola that meets all of these requirements: Vertex below the x-axis Concave up One positive x-intercept One negative x-intercept Line of symmetry at x = 2. Unit 8: Introduction to Quadratics & Their Transformations S.30

3 Lesson Summary Quadratic functions create a symmetrical curve with its highest (maximum) or lowest (minimum) point corresponding to its vertex and an axis of symmetry passing through the vertex when graphed. The xx-coordinate of the vertex is the average of the xx-coordinates of the zeros or any two symmetric points on the graph. When the leading coefficient is a negative number, the graph opens down, and its end behavior is that both ends move towards negative infinity. If the leading coefficient is positive, the graph opens up, and both ends move towards positive infinity. Homework Problem Set 1. Khaya stated that every yy-value of the graph of a quadratic function has two different xx-values. Do you agree or disagree with Khaya? Explain your answer. 2. Is it possible for the graphs of two different quadratic functions to each have xx = 3 as its line of symmetry and both have a maximum at yy = 5? Explain and support your answer with a sketch of the graphs. Unit 8: Introduction to Quadratics & Their Transformations S.31

4 3. Use the graphs of quadratic functions (Graph A and Graph B) to fill in the table and answer the questions on the following page. xx ff(xx) 1 8 Graph A xx ff(xx) Graph B Unit 8: Introduction to Quadratics & Their Transformations S.32

5 Use your graphs and tables of values from Problem 3 to fill in the blanks in the table below. Graph A Graph B 4. xx-intercepts 5. Vertex Sign of the Leading Coefficient Vertex Represents a Minimum or Maximum? Find ff( 1) and ff(5). Find ff( 1) and ff( 3). 8. Points of Symmetry Is ff(7) greater than or less than 8? Explain ff(2) = 12. Predict the value for ff( 6) and explain your answer. On what intervals of the domain is the function depicted by the graph increasing? On what intervals of the domain is the function depicted by the graph increasing? 9. Increasing and Decreasing Intervals On what intervals of the domain is the function depicted by the graph decreasing? On what intervals of the domain is the function depicted by the graph decreasing? Unit 8: Introduction to Quadratics & Their Transformations S.33

6 10. Consider the following key features discussed in this lesson for the four graphs of quadratic functions below: xx-intercepts, yy-intercept, line of symmetry, vertex, and end behavior. Graph A Graph B Graph C Graph D A. Which key features of a quadratic function do Graphs A and B have in common? Which features are not shared? B. Compare Graphs A and C, and explain the differences and similarities between their key features. C. Compare Graphs A and D, and explain the differences and similarities between their key features. D. What do all four of the graphs have in common? Unit 8: Introduction to Quadratics & Their Transformations S.34

7 11. Use the symmetric properties of quadratic functions to sketch the graph of the function at the right, given these points and given that the vertex of the graph is the point (0, 5). (0, 5) (1, 3) (2, 3) 12. If possible, find the equation for the axis of symmetry for the graph of a quadratic function with the given pair of coordinates. If not possible, explain why. A. (3, 10) (15, 10) B. ( 2, 6) (6,4) SPIRAL REVIEW Module 2, Unit 3, Lesson 5 For each problem below, use distribution and then combine like terms (x + 3) 14. 5(x + 4) + 2(x + 1) Unit 8: Introduction to Quadratics & Their Transformations S.35

8 15. 2(x + 1) 3(x 7) 16. 3(x 2) + 3x 17. 1(x + 1) + 2(x + 1) 18. 5(3x + 4) SPIRAL REVIEW Module 3, Unit 5, Lesson 5 Simplify each expression so that there are no negative exponents x x a 2 a 3 a 21. b 4 b 3 b x 2x z z z 24. g 2 g ( ab ) x x 27. w 2 z ( y ) ( y ) 29. p p p ( r ) ( r ) Unit 8: Introduction to Quadratics & Their Transformations S.36