Chap5 Section3

Elementary and Intermediate Algebra: Graphs & Models (3rd Edition)

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Section 5.3 Zeros of the Quadratic 473 Version: Fall 2007 5.3 Exercises In Exercises 1 - 8 , factor the given qua- dratic polynomial. 1. x 2 + 9 x + 14 2. x 2 + 6 x + 5 3. x 2 + 10 x + 9 4. x 2 + 4 x 21 5. x 2 4 x 5 6. x 2 + 7 x 8 7. x 2 7 x + 12 8. x 2 + 5 x 24 In Exercises 9 - 16 , find the zeros of the given quadratic function. 9. f ( x ) = x 2 2 x 15 10. f ( x ) = x 2 + 4 x 32 11. f ( x ) = x 2 + 10 x 39 12. f ( x ) = x 2 + 4 x 45 13. f ( x ) = x 2 14 x + 40 14. f ( x ) = x 2 5 x 14 15. f ( x ) = x 2 + 9 x 36 16. f ( x ) = x 2 + 11 x 26 Copyrighted material. See: http://msenux.redwoods.edu/IntAlgText/ 1 In Exercises 17 - 22 , perform each of the following tasks for the quadratic func- tions. i. Load the function into Y1 of the Y= of your graphing calculator. Adjust the window parameters so that the vertex is visible in the viewing window. ii. Set up a coordinate system on your homework paper. Label and scale each axis with xmin, xmax, ymin, and ymax. Make a reasonable copy of the image in the viewing window of your calcu- lator on this coordinate system and label it with its equation. iii. Use the zero utility on your graph- ing calculator to find the zeros of the function. Use these results to plot the x -intercepts on your coordinate system and label them with their co- ordinates. iv. Use a strictly algebraic technique (no calculator) to find the zeros of the given quadratic function. Show your work next to your coordinate system. Be stubborn! Work the problem until your algebraic and graphically zeros are a reasonable match. 17. f ( x ) = x 2 + 5 x 14 18. f ( x ) = x 2 + x 20 19. f ( x ) = x 2 + 3 x + 18 20. f ( x ) = x 2 + 3 x + 40 21. f ( x ) = x 2 16 x 36 22. f ( x ) = x 2 + 4 x 96
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474 Chapter 5 Quadratic Functions Version: Fall 2007 In Exercises 23 - 30 , 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. Re- member to draw all lines with a ruler. ii. Use the technique of completing the square to place the quadratic func- tion in vertex form. Plot the vertex on your coordinate system and label it with its coordinates. Draw the axis of symmetry on your coordinate sys- tem and label it with its equation. iii. Use a strictly algebraic technique (no calculators) to find the x -intercepts of the graph of the given quadratic function. Plot them on your coor- dinate system and label them with their coordinates. iv. Find the y -intercept of the graph of the quadratic function. Plot the y - intercept on your coordinate system and its mirror image across the axis of symmetry, then label these points with their coordinates. v. Using all the information plotted, draw the graph of the quadratic function and label it with the vertex form of its equation. Use interval notation to describe the domain and range of the quadratic function. 23. f ( x ) = x 2 + 2 x 8 24. f ( x ) = x 2 6 x + 8 25. f ( x ) = x 2 + 4 x 12 26. f ( x ) = x 2 + 8 x + 12 27. f ( x ) = x 2 2 x + 8 28. f ( x ) = x 2 2 x + 24 29. f ( x ) = x 2 8 x + 48 30. f ( x ) = x 2 8 x + 20 In Exercises 31 - 38 , factor the given qua- dratic polynomial.
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