Practice and Problem-Solving Exercises

A Practice

See Problem 1.

Solve each equation by factoring. Check your answers.

9. x 2 + 6 x + 8 = 0 x squared , plus 6 x plus 8 equals 0
10. x 2 + 18 = 9 x x squared , plus 18 equals 9 x
11. 2 x 2 − x = 3 2 x squared , minus x equals 3
12. x 2 − 10 x + 25 = 0 x squared , minus 10 x plus 25 equals 0
13. 2 x 2 + 6 x = − 4 2 x squared , plus 6 x equals negative 4
14. 3 x 2 = 16 x + 12 3 x squared , equals 16 x plus 12
15. x 2 − 4 x = 0 x squared , minus 4 x equals 0
16. 6 x 2 + 4 x = 0 6 x squared , plus 4 x equals 0
17. 2 x 2 = 8 x 2 x squared , equals 8 x

See Problem 2.

Graphing Calculator Solve each equation using tables. Give each answer to at most two decimal places.

18. x 2 + 5 x + 3 = 0 x squared , plus 5 x plus 3 equals 0
19. x 2 − 11 x + 24 = 0 x squared , minus 11 x plus 24 equals 0
20. x 2 − 7 x = 11 x squared , minus 7 x equals 11
21. 2 x 2 − x = 2 2 x squared , minus x equals 2
22. x 2 − 16 x = 36 x squared , minus 16 x equals 36
23. x 2 + 6 x = 40 x squared , plus 6 x equals 40
24. 4 x 2 = x + 3 4 x squared , equals x plus 3
25. 5 x 2 + x = 4 5 x squared , plus x equals 4
26. 10 x 2 + 3 = 11 x 10 x squared , plus 3 equals 11 x

See Problem 3.

Graphing Calculator Solve each equation by graphing. Give each answer to at most two decimal places.

27. 6 x 2 = − 19 x − 15 6 x squared , equals negative 19 x minus 15
28. 3 x 2 − 5 x − 4 = 0 3 x squared , minus 5 x minus 4 equals 0
29. 5 x 2 − 7 x − 3 = 8 5 x squared , minus 7 x minus 3 equals 8
30. 6 x 2 + 31 x = 12 6 x squared , plus 31 x equals 12
31. 1 = 4 x 2 + 3 x 1 equals , 4 x squared , plus 3 x
32. 1 2 x 2 − x = 8 1 half , x squared , minus x equals 8
33. x 2 = 4 x + x squared , equals 4 x plus  8
34. x 2 + 4 x = 6 x squared , plus 4 x equals 6
35. 2 x 2 − 2 x − 5 = 0 2 x squared , minus 2 x minus 5 equals 0

    See Problem 4.

36. Physics An object is dropped from a height of 1700 ft above the ground. The function h = − 16 t 2 + 1700 h equals negative 16 , t squared , plus , 1700  gives the object's height h in feet during free fall at t seconds.

    1. When will the object be 1000 ft above the ground?
    2. When will the object be 940 ft above the ground?
    3. What are a reasonable domain and range for the function h?

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