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**Unformatted text preview: **Section 5.1 The Parabola 433 Version: Fall 2007 5.1 Exercises In Exercises 1- 6 , sketch the image of your calculator screen on your homework paper. Label and scale each axis with xmin, xmax, ymin, and ymax. Label each graph with its equation. Remember to use a ruler to draw all lines, including axes. 1. Use your graphing calculator to sketch the graphs of f ( x ) = x 2 , g ( x ) = 2 x 2 , and h ( x ) = 4 x 2 on one screen. Write a short sentence explaining what you learned in this exercise. 2. Use your graphing calculator to sketch the graphs of f ( x ) =- x 2 , g ( x ) =- 2 x 2 , and h ( x ) =- 4 x 2 on one screen. Write a short sentence explaining what you learned in this exercise. 3. Use your graphing calculator to sketch the graphs of f ( x ) = x 2 , g ( x ) = ( x- 2) 2 , and h ( x ) = ( x- 4) 2 on one screen. Write a short sentence explaining what you learned in this exercise. 4. Use your graphing calculator to sketch the graphs of f ( x ) = x 2 , g ( x ) = ( x + 2) 2 , and h ( x ) = ( x + 4) 2 on one screen. Write a short sentence explaining what you learned in this exercise. 5. Use your graphing calculator to sketch the graphs of f ( x ) = x 2 , g ( x ) = x 2 + 2 , and h ( x ) = x 2 + 4 on one screen. Write a short sentence explaining what you learned in this exercise. Copyrighted material. See: http://msenux.redwoods.edu/IntAlgText/ 1 6. Use your graphing calculator to sketch the graphs of f ( x ) = x 2 , g ( x ) = x 2- 2 , and h ( x ) = x 2- 4 on one screen. Write a short sentence explaining what you learned in this exercise. In Exercises 7- 14 , write down the given quadratic function on your homework pa- per, then state the coordinates of the ver- tex. 7. f ( x ) =- 5( x- 4) 2- 5 8. f ( x ) = 5( x + 3) 2- 7 9. f ( x ) = 3( x + 1) 2 10. f ( x ) = 7 5 y x + 5 9 y 2- 3 4 11. f ( x ) =- 7( x- 4) 2 + 6 12. f ( x ) =- 1 2 y x- 8 9 y 2 + 2 9 13. f ( x ) = 1 6 y x + 7 3 y 2 + 3 8 14. f ( x ) =- 3 2 y x + 1 2 y 2- 8 9 In Exercises 15- 22 , state the equation of the axis of symmetry of the graph of the given quadratic function. 15. f ( x ) =- 7( x- 3) 2 + 1 16. f ( x ) =- 6( x + 8) 2 + 1 434 Chapter 5 Quadratic Functions Version: Fall 2007 17. f ( x ) =- 7 8 y x + 1 4 y 2 + 2 3 18. f ( x ) =- 1 2 y x- 3 8 y 2- 5 7 19. f ( x ) =- 2 9 y x + 2 3 y 2- 4 5 20. f ( x ) =- 7( x + 3) 2 + 9 21. f ( x ) =- 8 7 y x + 2 9 y 2 + 6 5 22. f ( x ) = 3( x + 3) 2 + 6 In Exercises 23- 36 , perform each of the following tasks for the given quadratic function. i. Set up a coordinate system on graph paper. Label and scale each axis. ii. Plot the vertex of the parabola and label it with its coordinates. iii. Draw the axis of symmetry and label it with its equation. iv. Set up a table near your coordinate system that contains exact coordinates of two points on either side of the axis of symmetry. Plot them on your co- ordinate system and their “mirror im- ages” across the axis of symmetry....

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