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**Unformatted text preview: **Section 5.6 Optimization 541 Version: Fall 2007 5.6 Exercises 1. Find the exact maximum value of the function f ( x ) = − x 2 − 3 x . 2. Find the exact maximum value of the function f ( x ) = − x 2 − 5 x − 2. 3. Find the vertex of the graph of the function f ( x ) = − 3 x 2 − x − 6. 4. Find the range of the function f ( x ) = − 2 x 2 − 9 x + 2. 5. Find the exact maximum value of the function f ( x ) = − 3 x 2 − 9 x − 4. 6. Find the equation of the axis of sym- metry of the graph of the function f ( x ) = − x 2 − 5 x − 9. 7. Find the vertex of the graph of the function f ( x ) = 3 x 2 + 3 x + 9. 8. Find the exact minimum value of the function f ( x ) = x 2 + x + 1. 9. Find the exact minimum value of the function f ( x ) = x 2 + 9 x . 10. Find the range of the function f ( x ) = 5 x 2 − 3 x − 4. 11. Find the range of the function f ( x ) = − 3 x 2 + 8 x − 2. 12. Find the exact minimum value of the function f ( x ) = 2 x 2 + 5 x − 6. 13. Find the range of the function f ( x ) = 4 x 2 + 9 x − 8. 14. Find the exact maximum value of the function f ( x ) = − 3 x 2 − 8 x − 1. Copyrighted material. See: http://msenux.redwoods.edu/IntAlgText/ 1 15. Find the equation of the axis of symmetry of the graph of the function f ( x ) = − 4 x 2 − 2 x + 9. 16. Find the exact minimum value of the function f ( x ) = 5 x 2 + 2 x − 3. 17. A ball is thrown upward at a speed of 8 ft/s from the top of a 182 foot high building. How many seconds does it take for the ball to reach its maximum height? Round your answer to the nearest hun- dredth of a second. 18. A ball is thrown upward at a speed of 9 ft/s from the top of a 143 foot high building. How many seconds does it take for the ball to reach its maximum height? Round your answer to the nearest hun- dredth of a second. 19. A ball is thrown upward at a speed of 52 ft/s from the top of a 293 foot high building. What is the maximum height of the ball? Round your answer to the nearest hundredth of a foot. 20. A ball is thrown upward at a speed of 23 ft/s from the top of a 71 foot high building. What is the maximum height of the ball? Round your answer to the nearest hundredth of a foot. 21. Find two numbers whose sum is 20 and whose product is a maximum. 22. Find two numbers whose sum is 36 and whose product is a maximum. 23. Find two numbers whose difference is 12 and whose product is a minimum. 542 Chapter 5 Quadratic Functions Version: Fall 2007 24. Find two numbers whose difference is 24 and whose product is a minimum. 25. One number is 3 larger than twice a second number. Find two such numbers so that their product is a minimum. 26. One number is 2 larger than 5 times a second number. Find two such num- bers so that their product is a minimum....

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