Practice and Problem-Solving Exercises

A Practice

See Problem 1.

Identify the vertex, the axis of symmetry, the maximum or minimum value, and the range of each parabola.

8. y = x 2 + 2 x + 1 y equals , x squared , plus 2 x plus 1
9. y = − x 2 + 2 x + 1 y equals negative , x squared , plus 2 x plus 1
10. y = x 2 + 4 x + 1 y equals , x squared , plus 4 x plus 1
11. y = − x 2 + 2 x + 5 y equals negative , x squared , plus 2 x plus 5
12. y = 3 x 2 − 4 x − 2 y equals , 3 x squared , minus 4 x minus 2
13. y = − 2 x 2 − 3 x + 4 y equals negative 2 , x squared , minus 3 x plus 4
14. y = 2 x 2 − 6 x + 3 y equals , 2 x squared , minus 6 x plus 3
15. y = − x 2 − x y equals negative , x squared , minus x
16. y = 2 x 2 + 5 y equals , 2 x squared , plus 5

See Problem 2.

Graph each function.

17. y = x 2 + 6 x + 9 y equals , x squared , plus 6 x plus 9
18. y = − x 2 − 3 x + 6 y equals negative , x squared , minus 3 x plus 6
19. y = 2 x 2 + 4 x y equals , 2 x squared , plus 4 x
20. y = 4 x 2 − 12 x + 9 y equals , 4 x squared , minus 12 x plus 9
21. y = − 6 x 2 − 12 x − 1 y equals negative 6 , x squared , minus 12 x minus 1
22. y = − 3 4 x 2 + 6 x + 6 y equals negative , 3 fourths , x squared , plus 6 x plus 6
23. y = 3 x 2 − 12 x + 10 y equals , 3 x squared , minus 12 x plus 10
24. y = 1 2 x 2 + 2 x − 8 y equals , 1 half , x squared , plus 2 x minus 8
25. y = − 4 x 2 − 24 x − 36 y equals negative 4 , x squared , minus 24 x minus 36

See Problem 3.

Write each function in vertex form.

26. y = x 2 − 4 x + 6 y equals , x squared , minus 4 x plus 6
27. y = x 2 + 2 x + 5 y equals , x squared , plus 2 x plus 5
28. y = 4 x 2 + 7 x y equals , 4 x squared , plus 7 x
29. y = 2 x 2 − 5 x + 12 y equals , 2 x squared , minus 5 x plus 12
30. y = − 2 x 2 + 8 x + 3 y equals negative 2 , x squared , plus 8 x plus 3
31. y = 9 4 x 2 + 3 x − 1 y equals , 9 fourths , x squared , plus 3 x minus 1

    See Problem 4.

32. Economics A model for a company's revenue from selling a software package is R = − 2 . 5 p 2 + 500 p , r equals negative 2 . 5 , p squared , plus 500 p comma  where p is the price in dollars of the software. What price will maximize revenue? Find the maximum revenue.

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