1 How is the graph of y equals negative 2 x squared minus 5 different from the graph of y equals negative 2 x squared?
A. It is shifted 5 units up.
B. It is shifted 5 units down.
C. It is shifted 5 units left.
D. It is shifted 5 units right.
2 A model rocket is launched from a roof into a large field. The path of the rocket can be modeled by the equation y equals negative 0.06 x squared plus 9.6 x plus 5.4 where x is the horizontal distance, in meters, from the starting point on the roof and y is the height, in meters, of the rocket above the ground.
3 How far horizontally from its starting point will the rocket land? Round your answer to the nearest hundredth.
A. 4.30 m
B. 160.56 m
C. 161.12 m
D. 13.94 m
4 Which of the following functions has a rate of change that stays the same?
A. y equals one third x squared
B. y equals 2 superscript x baseline
C. y equals negative 7 x plus 9
D. y equals x squared plus 1
5 How many real-number solutions does the equation have?
0 equals negative 7 lower x squared plus 6 lower x plus 3
A. one solution
B. two solutions
C. no solutions
D. infinitely many solutions\
6 How many real-number solutions does the equation have?
0 equals 3 x squared plus 18 x plus 27
A. one solution
B. two solutions
C. no solutions
D. infinitely many solutions
7 Graph the set of points. Which model is most appropriate for the set?
(negative 6, 0), (negative 4, 2), (negative 3, 3), (2, 8)
8 What type of equation will best fit the data below?
a coordinate plane with points plotted that form a U shape.
A. linear
B. quadratic
C. exponential
9 Water is added to two containers for 16 minutes. The equations below model the ounces of water, y, in each container after x minutes. At the time after the start when the containers hold the same amount of water, how much water do they hold?
Container A: y equals 16 x plus 104
Container B: y equals negative 2 x squared plus 40x plus 160
A. 360 ounces
B. 328 ounces
C. 232 ounces
D. 136 ounces
10 If an object is dropped from a height of 200 feet, the function h of t equals negative 16t squared plus 200 gives the height of the object after t seconds. Approximately, when will the object hit the ground?
A. 200.00 seconds
B. 184.00 seconds
C. 3.54 seconds
D. 0.78 seconds
11 A catapult launches a boulder with an upward velocity of 122 feet per second. The height of the boulder, (h), in feet after t seconds is given by the function h of t equals negative 16t squared plus 122t plus 10 . How long does it take the boulder to reach its maximum height? What is the boulder’s maximum height? Round to the nearest hundredth, if necessary.
A. Reaches a maximum height of 15.42 feet after 7.71 seconds.
B. Reaches a maximum height of 7.71 feet after 3.81 seconds.
C. Reaches a maximum height of 242.56 feet after 7.62 seconds.
D. Reaches a maximum height of 242.56 feet after 3.81 seconds.
Use the graph of f (x) to find the solutions to the equation f (x) = 0.
12 A coordinate plane with parabola opening down. The y-intercept is 20 and the x-intercepts are 7 and negative 4.
A. two solutions: x = negative 4, 7
B. two solutions: x = 4 and negative 7
C. one solution: x = 28
D. no solutions
13 What are the solutions of the equation 2 x squared equals 8? Use a graph of a related function whose roots answer the question.
A. An upward facing parabola passes through points left parenthesis negative 2 comma 0 right parenthesis, left parenthesis 0 comma negative 4 right parenthesis, and left parenthesis 2 comma 0 right parenthesis.
There are two solutions: x equals plus or minus 2
B. An upward facing parabola passes through points left parenthesis negative 2 comma 8 right parenthesis, left parenthesis 0 comma 4 right parenthesis, and left parenthesis 2 comma 8 right parenthesis.
There are no solutions.
C. An upward facing parabola passes through points left parenthesis negative 2 comma 2 right parenthesis, left parenthesis 0 comma negative 2 right parenthesis, and left parenthesis 2 comma 2 right parenthesis.
There are two solutions: x equals plus or minus start root 2 end root
D. An upward facing parabola passes through points left parenthesis negative 4 comma 0 right parenthesis, left parenthesis 0 comma negative 8 right parenthesis, and left parenthesis 4 comma 0 right parenthesis.
There are two solutions: x equals plus or minus 4
14 Solve the equation using the Zero Product Property.
The quantity 2x plus 6 times the quantity 3x minus 6 equals 0.
A. 3 and 2
B. negative 3 comma negative 2
C. negative 3 and 2
D. 3 and negative 2
15 What are the solutions of the equation?
0 equals x squared minus 2x minus 24
A. x = 6, 4
B. x = negative 6, negative 4
C. x = negative 6, 4
D. x = 6 and negative 4
16 A community group is planning the expansion of a square flower garden in a city park. If each side of the original garden is increased by 9 meters, the new total area of the garden will be 169 square meters. Find the length of each side of the original garden.
A. 9 m
B. 13 m
C. 2 m
D. 4 m
17 What is the value of c so that x2 + 15x + c is a perfect square trinomial?
A. 30
B. fifteen-halves
C. fifteen-fourths
D. 225-fourths
18 Solve the equation by completing the square. Round to the nearest hundredth if necessary.
x squared plus 10 x equals 18
A. negative 11.56 comma 1.56
B. 11.56, 1.56
C. negative 11.56, negative 1.56
D. 11.56, negative 1.56
19 Solve the equation by completing the square.
x squared plus 9 x minus 14 equals 0
A. 10.35, 1.35
B. 10.35, negative 1 point 35
C. negative 10.35, negative 1.35
D. negative 10.35, 1.35
20 Use the quadratic formula to solve the equation. If necessary, round to the nearest hundredth.
x squared plus 3 equals negative 4 x
A. 1, 3
B. negative 1, negative 3
C. 1, negative 3
D. negative 1, 3
21 Which kind of function best models the data in the table? Use differences or ratios.
x
y
0 1.3
1 7.8
2 46.8
3 280.8
4 1684.8
A. linear
B. quadratic
C. exponential
D. none of the above
1. B. It is shifted 5 units down.
2. 161.12 m
3. B. y equals 2 superscript x baseline
4. A. y equals one third x squared
5. C. no solutions
6. C. no solutions
7. Quadratic
8. Quadratic
9. C. 232 ounces
10. C. 3.54 seconds
11. B. Reaches a maximum height of 7.71 feet after 3.81 seconds.
12. A. two solutions: x = negative 4, 7
13. A. An upward facing parabola passes through points left parenthesis negative 2 comma 0 right parenthesis, left parenthesis 0 comma negative 4 right parenthesis, and left parenthesis 2 comma 0 right parenthesis. There are two solutions: x equals plus or minus 2.
14. D. 3 and negative 2
15. A. x = 6, 4
16. B. 13 m
17. 225-fourths
18. B. 11.56, 1.56
19. C. negative 10.35, negative 1.35
20. D. negative 1, 3
21. Exponential