Practice and Problem-Solving Exercises

A Practice

See Problem 1.

Identify the vertex of each graph. Tell whether it is a minimum or a maximum.

See Problem 2.

Graph each function. Then identify the domain and range of the function.

10. y = − 4 x 2 y equals negative , 4 x squared
11. f ( x ) = 1 . 5 x 2 f open x close equals 1 . , 5 x squared
12. f ( x ) = 3 x 2 f open x close equals , 3 x squared
13. f ( x ) = 2 3 x 2 f , open x close , equals , 2 thirds , x squared
14. y = − 1 2 x 2 y equals negative , 1 half , x squared
15. y = − 1 3 x 2 y equals negative , 1 third , x squared

See Problem 3.

Order each group of quadratic functions from widest to narrowest graph.

16. y = 3 x 2 , y = 2 x 2 , y = 4 x 2 y equals , 3 x squared , comma y equals , 2 x squared , comma y equals , 4 x squared
17. f ( x ) = 5 x 2 , f ( x ) = − 3 x 2 , f ( x ) = x 2 f open x close equals , 5 x squared , comma f open x close equals negative , 3 x squared , comma f open x close equals , x squared
18. y = − 1 2 x 2 , y = 5 x 2 , y = − 1 4 x 2 y equals negative , 1 half , x squared , comma . y equals , 5 x squared , comma . y equals negative , 1 fourth , x squared
19. f ( x ) = − 2 x 2 , f ( x ) = − 2 3 x 2 , f ( x ) = − 4 x 2 f open x close equals negative , 2 x squared , comma . f , open x close , equals negative , 2 thirds , x squared , comma . f open x close equals negative , 4 x squared

See Problem 4.

Graph each function.

20. f ( x ) = x 2 + 4 f open x close equals , x squared , plus 4
21. y = x 2 − 7 y equals , x squared , minus 7
22. y = 1 2 x 2 + 2 y equals , 1 half , x squared , plus 2
23. f ( x ) = − x 2 − 3 f open x close equals negative , x squared , minus 3
24. y = − 2 x 2 + 4 y equals negative , 2 x squared , plus 4
25. f ( x ) = 4 x 2 − 5 f open x close equals , 4 x squared , minus 5

See Problem 5.

26. Dropped Object A person walking across a bridge accidentally drops an orange into the river below from a height of 40 ft. The function h = − 16 t 2 + 40 h equals negative , 16 t squared , plus 40  gives the orange's approximate height h above the water, in feet, after t seconds. Graph the function. In how many seconds will the orange hit the water?
27. Nature A bird drops a stick to the ground from a height of 80 ft. The function h = − 16 t 2 + 80 h equals negative , 16 t squared , plus 80  gives the stick's approximate height h above the ground, in feet, after t seconds. Graph the function. At about what time does the stick hit the ground?

B Apply

28. Error Analysis Describe and correct the error made in graphing the function y = − 2 x 2 + 1 . y equals negative , 2 x squared , plus 1 .

    

Identify the domain and range of each function.

29. f ( x ) = 3 x 2 + 6 f open x close equals , 3 x squared , plus 6
30. y = − 2 x 2 − 1 y equals negative , 2 x squared , minus 1
31. y = − 3 4 x 2 − 9 y equals negative , 3 fourths , x squared , minus 9
32. y = 2 3 x 2 + 12 y equals , 2 thirds , x squared , plus 12

33. Writing What information do the numbers a and c give you about the graph of y = a x 2 + c ? y equals , eh x squared , plus c question mark

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