9 Chapter Test

Do you know HOW?

Graph each function.

1. y = 3 x 2 − 7 y equals , 3 x squared , minus 7
2. y = − x 2 − 2 y equals negative . x squared , minus 2
3. y = − 2 x 2 + 10 x − 1 y equals negative , 2 x squared , plus 10 x minus 1
4. y = x 2 − 3 x + 2 y equals . x squared , minus 3 . x plus 2

Solve each equation.

5. x 2 + 11 x − 26 = 0 x squared , plus 11 . x minus 26 equals 0
6. x 2 − 25 = 0 x squared , minus 25 equals 0
7. x 2 − 19 x + 80 = − 8 x squared , minus 19 . x plus 80 equals negative 8
8. x 2 − 5 x = − 4 x x squared , minus 5 . x equals negative 4 x
9. 4 x 2 − 100 = 0 4 x squared , minus 100 equals 0
10. 5 x 2 − 8 x = 8 − 5 x 5 x squared , minus 8 x equals 8 minus 5 x
11. Design You are creating a rectangular banner for a school pep rally. You have 100  ft 2 100 , ft squared  of paper, and you want the length to be 15 ft longer than the width. What should be the dimensions of the banner?

Find the number of real-number solutions of each equation.

12. x 2 + 4 x = − 4 x squared , plus 4 . x equals negative 4
13. x 2 + 8 = 0 x squared , plus 8 equals 0
14. 3 x 2 − 9 x = − 5 3 x squared , minus 9 x equals negative 5

Solve each equation. If necessary, round to the nearest hundredth.

15. − 3 x 2 + 7 x = − 10 negative , 3 x squared , plus 7 x equals negative 10
16. x 2 + 4 x = 1 x squared , plus 4 . x equals 1
17. 12 x 2 + 16 x − 28 = 0 12 x squared , plus 16 x minus 28 equals 0
18. x 2 + 6 x + 9 = 25 x squared , plus 6 . x plus 9 equals 25
19. Vertical Motion You throw a ball upward. Its height h, in feet, after t seconds can be modeled by the function h = − 16 t 2 + 30 t + 6 . h equals negative , 16 t squared , plus 30 t plus 6 .  After how many seconds will it hit the ground?

20. Identify the graph below as linear, quadratic, or exponential. Write an equation that models the data points shown.

    

Solve each system.

21. y = x 2 + 3 x − 23 y = 25 − 5 x table with 2 rows and 1 column , row1 column 1 , y equals , x squared , plus 3 x minus 23 , row2 column 1 , y equals 25 minus 5 x , end table
22. y = x 2 + 2 x − 2 y = x + 10 table with 2 rows and 1 column , row1 column 1 , y equals , x squared , plus 2 x minus 2 , row2 column 1 , y equals x plus 10 , end table

Do you UNDERSTAND?

23. Writing Explain what you can determine about the shape of a parabola from its equation alone.
24. Open-Ended Write an equation of a parabola that has two x-intercepts and a maximum value. Include a graph of your parabola.
25. Find a nonzero value of k such that k x 2 − 10 x + 25 = 0 k x squared , minus 10 x plus 25 equals 0  has one real-number solution.

26. Reasoning The graph of a quadratic function y = a x 2 + b x + c y equals , eh x squared , plus b x plus c  is shown. What do you know about the values of a, b, and c just by looking at the graph?

    

27. Geometry Suppose a rectangle has an area of 60  ft 2 60 , ft squared  and dimensions, in feet, of x and x + 1 . x plus 1 .
    1. Estimate each dimension of the rectangle to the nearest foot.
    2. Write a quadratic equation and use the quadratic formula to find each dimension to the nearest hundredth of a foot.

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