9 Mid-Chapter Quiz

Do you know HOW?

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

1. y = 2 x 2 , y = 0 . 5 x 2 , y = − x 2 y equals , 2 x squared , comma y equals 0 . , 5 x squared , comma y equals negative , x squared
2. f ( x ) = 4 x 2 , f ( x ) = 2 3 x 2 , f ( x ) = 3 x 2 f open x close equals , 4 x squared , comma . f , open x close , equals , 2 thirds , x squared , comma . f open x close equals , 3 x squared
3. f ( x ) = 0 . 6 x 2 , f ( x ) = 0 . 3 x 2 , f ( x ) = 0 . 2 x 2 f open x close equals 0 . , 6 x squared , comma f open x close equals 0 . , 3 x squared , comma f open x close equals 0 . , 2 x squared
4. y = − 2 x 2 , y = x 2 , y = − 0 . 25 x 2 y equals negative , 2 x squared , comma y equals , x squared , comma , y equals negative 0 . , 25 x squared

Graph each function. Label the axis of symmetry and the vertex.

5. y = 1 2 x 2 y equals , 1 half , x squared
6. y = − 2 x 2 − 1 y equals negative , 2 x squared , minus 1
7. y = 3 x 2 − 6 x y equals , 3 x squared , minus 6 x
8. y = x 2 + 2 x + 4 y equals . x squared , plus 2 . x plus 4
9. y = − 0 . 5 x 2 + 2 x + 1 y equals negative 0 . , 5 x squared , plus 2 x plus 1

Solve each equation by graphing the related function. If the equation has no real-number solution, write no solution.

10. x 2 − 16 = 0 x squared , minus 16 equals 0
11. x 2 + 9 = 0 x squared , plus 9 equals 0
12. 0.25 x 2 = 0 0.25 , x squared . equals 0

Solve each equation by finding square roots. If the equation has no real-number solution, write no solution.

13. m 2 = 81 m squared , equals 81
14. t 2 − 7 = − 18 t squared , minus 7 equals . minus 18
15. 5 r 2 − 180 = 0 5 r squared , minus 180 equals 0
16. 36 n 2 = 9 36 n squared , equals 9
17. Sewing You have 324  ft 2 324 , ft squared  of fabric to make a circular play parachute for kids. What is the radius of the largest parachute you could make? Round to the nearest tenth of a foot.

Solve by factoring.

18. b 2 + 3 b − 4 = 0 b squared , plus 3 . b minus 4 equals 0
19. n 2 + n − 12 = 0 n squared , plus , n minus 12 equals 0
20. 2 x 2 − 5 x − 3 = 0 2 x squared , minus 5 x minus 3 equals 0
21. t 2 − 3 t = 28 t squared , minus 3 . t equals 28
22. 3 n 2 = 6 n 3 n squared , equals 6 n
23. Construction You are building a rectangular planter for your school garden. You want the area of the bottom to be 90  ft 2 . 90 , ft squared , .  You want the length of the planter to be 3 ft longer than twice its width. What should the dimensions of the bottom of the planter be?

Do you UNDERSTAND?

24. Writing Describe the steps you would use to graph the function y = 2 x 2 + 5 . y equals , 2 x squared , plus 5 .
25. Reasoning Does the value of c in the quadratic function y = a x 2 + b x + c y equals , eh x squared , plus b x plus c  affect the horizontal position of the vertex of the graph? Explain why or why not.
26. Writing Describe how the graph of y = 3 x 2 y equals , 3 x squared  differs from the graph of y = x 2 . y equals , x squared , .

Open-Ended Give an example of a quadratic function that matches each description.

27. The axis of symmetry is to the left of the y-axis.
28. Its graph lies entirely below the x-axis.
29. Its graph opens upward and has its vertex at (0, 0).
30. 1. Solve x 2 − 4 = 0 x squared , minus 4 equals . 0  and 2 x 2 − 8 = 0 2 x squared , minus 8 equals 0  by graphing their related functions.
    2. Reasoning Why does it make sense that the graphs have the same x-intercepts?

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