Practice and Problem-Solving Exercises

A Practice

See Problem 1.

Graph each function.

7. y = − x 2 y equals negative , x squared
8. f ( x ) = 5 x 2 f open x close equals , 5 x squared
9. y = 2 5 x 2 y equals , 2 fifths , x squared
10. y = 2 x 2 y equals , 2 x squared
11. f ( x ) = 2 1 4 x 2 f open x close equals , 2 , and 1 fourth . x squared
12. y = − 4 9 x 2 y equals negative , 4 ninths , x squared
13. y = − 7 x 2 y equals negative 7 , x squared
14. f ( x ) = 3 2 5 x 2 f open x close equals , 3 , and 2 fifths . x squared

See Problem 2.

Graph each function. Describe how it was translated from f ( x ) = x 2 . f open x close equals , x squared , .

15. f ( x ) = x 2 + 3 f open x close equals , x squared , plus 3
16. f ( x ) = ( x − 2 ) 2 f open x close equals open x minus 2 , close squared
17. f ( x ) = x 2 − 6 f open x close equals , x squared , minus 6
18. f ( x ) = ( x + 3 ) 2 f open x close equals open x plus 3 , close squared
19. f ( x ) = x 2 − 9 f open x close equals , x squared , minus 9
20. f ( x ) = ( x + 5 ) 2 f open x close equals open x plus 5 , close squared
21. f ( x ) = x 2 + 1 . 5 f open x close equals , x squared , plus 1 . 5
22. f ( x ) = ( x − 2 . 5 ) 2 f open x close equals open x minus 2 . 5 , close squared

See Problem 3.

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

23. y = − 1.5 ( x + 20 ) 2 y equals negative 1.5 open x plus 20 , close squared
24. f ( x ) = 0 . 1 ( x − 3 . 2 ) 2 f open x close equals 0 . 1 open x minus 3 . 2 , close squared
25. f ( x ) = 24 ( x + 5 . 5 ) 2 f open x close equals 24 open x plus 5 . 5 , close squared
26. y = 0 . 0035 ( x + 1 ) 2 − 1 y equals 0 . , 0035 , open x plus 1 , close squared , minus 1
27. f ( x ) = − ( x − 4 ) 2 − 25 f open x close equals negative open x minus 4 , close squared , minus 25
28. y = ( x − 125 ) 2 + 125 y equals open x minus 125 , close squared , plus 125

See Problem 4.

Graph each function. Identify the axis of symmetry.

29. f ( x ) = ( x − 1 ) 2 + 2 f open x close equals open x minus 1 , close squared , plus 2
30. y = ( x + 3 ) 2 − 4 y equals open x plus 3 , close squared , minus 4
31. f ( x ) = 2 ( x − 2 ) 2 + 5 f open x close equals 2 open x minus 2 , close squared , plus 5
32. y = − 3 ( x + 7 ) 2 − 8 y equals negative 3 open x plus 7 , close squared , minus 8
33. y = − ( x − 1 ) 2 + 4 y equals negative open x minus 1 , close squared , plus 4
34. f ( x ) = − ( x − 7 ) 2 + 10 f open x close equals negative open x minus 7 , close squared , plus 10

See Problem 5.

Write a quadratic function to model each graph.

35. 
36. 
37. 

    B Apply

38. Think About a Plan A gardener is putting a wire fence along the edge of his garden to keep animals from eating his plants. If he has 20 meters of fence, what is the largest rectangular area he can enclose?
    • To find the area of a rectangle, what two quantities do you need? Choose one to be your variable and write the other in terms of this variable.
    • How can a graph help you solve this problem?
    • What quadratic function represents the area of the garden?
39. Manufacturing The equation for the cost in dollars of producing computer chips is C = 0 . 000015 x 2 − 0 . 03 x + 35 , c equals 0 . , 000015 . x squared , minus 0 . 03 x plus 35 comma  where x is the number of chips produced. Find the number of chips that minimizes the cost. What is the cost for that number of chips?

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