Chap5 Section4

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

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Section 5.4 The Quadratic Formula 497 Version: Fall 2007 5.4 Exercises In Exercises 1 - 8 , find all real solutions of the given equation. Use a calculator to approximate the answers, correct to the nearest hundredth (two decimal places). 1. x 2 = 36 2. x 2 = 81 3. x 2 = 17 4. x 2 = 13 5. x 2 = 0 6. x 2 = 18 7. x 2 = 12 8. x 2 = 3 In Exercises 9 - 16 , find all real solutions of the given equation. Use a calculator to approximate your answers to the nearest hundredth. 9. ( x 1) 2 = 25 10. ( x + 3) 2 = 9 11. ( x + 2) 2 = 0 12. ( x 3) 2 = 9 13. ( x + 6) 2 = 81 14. ( x + 7) 2 = 10 15. ( x 8) 2 = 15 16. ( x + 10) 2 = 37 Copyrighted material. See: 1 In Exercises 17 - 28 , perform each of the following tasks for the given quadratic function. i. Set up a coordinate system on a sheet of graph paper. Label and scale each axis. Remember to draw all lines with a ruler. ii. Place the quadratic function in ver- tex form. Plot the vertex on your co- ordinate system and label it with its coordinates. Draw the axis of sym- metry on your coordinate system and label it with its equation. iii. Use the quadratic formula to find the x -intercepts of the parabola. Use a calculator to approximate each inter- cept, correct to the nearest tenth, and use these approximations to plot the x -intercepts on your coordinate sys- tem. However, label each x -intercept with its exact coordinates. iv. Plot the y -intercept on your coordi- nate system and its mirror image across the axis of symmetry and label each with their coordinates. v. Using all of the information on your coordinate system, draw the graph of the parabola, then label it with the vertex form of the function. Use in- terval notation to state the domain and range of the quadratic function. 17. f ( x ) = x 2 4 x 8 18. f ( x ) = x 2 + 6 x 1 19. f ( x ) = x 2 + 6 x 3 20. f ( x ) = x 2 8 x + 1 21. f ( x ) = x 2 + 2 x + 10
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498 Chapter 5 Quadratic Functions Version: Fall 2007 22. f ( x ) = x 2 8 x 8 23. f ( x ) = x 2 8 x 9 24. f ( x ) = x 2 + 10 x 20 25. f ( x ) = 2 x 2 20 x + 40 26. f ( x ) = 2 x 2 16 x + 12 27. f ( x ) = 2 x 2 + 16 x + 8 28. f ( x ) = 2 x 2 24 x 52 In Exercises 29 - 32 , perform each of the following tasks for the given quadratic equation. i. Set up a coordinate system on a sheet of graph paper. Label and scale each axis. Remember to draw all lines with a ruler. ii. Show that the discriminant is nega- tive. iii. Use the technique of completing the square to put the quadratic function in vertex form. Plot the vertex on your coordinate system and label it with its coordinates. Draw the axis of symmetry on your coordinate system and label it with its equation. iv. Plot the y -intercept and its mirror image across the axis of symmetry on your coordinate system and label each with their coordinates. v. Because the discriminant is negative (did you remember to show that?), there are no x -intercepts. Use the given equation to calculate one addi- tional point, then plot the point and its mirror image across the axis of symmetry and label each with their coordinates.
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