1. A The graph would shift 3 units up.
How would the graph of the function y = x2 + 4 be affected if the function were changed to y = x2 + 1?
A The graph would shift 3 units up.
B The graph would shift 3 units down.
C The graph would shift 3 units to the right.
D The graph would shift 3 units to the left
Problem #1
Obj 5 - TAKS th [A.D1(C)]

2. Which graph shows a function y = x2 + c when c < –1?
Problem #2
Obj 5 - TAKS th [A.D1(C)]

3. Which expression is equivalent to ?
A 4x9
B 4x2
C 2x8
D 2x4
Problem #3
Obj 5 - TAKS th [A.D3(A)]

4. If y = x3, what is equivalent to x12? A y36 B y15 C y9 D y4
Problem #4
Obj 5 - TAKS th [A.D3(A)]

5. A. The graph of y = 4x2 is translated 8 units down.
What is the effect on the graph of the equation y = –4x2 when the equation is changed to y = 4x2?
A. The graph of y = 4x2 is translated 8 units down.
B. The graph of y = 4x2 is a reflection of y = –4x2 across the
x-axis.
C. The graph of y = 4x2 is translated 8 units up.
D. The graph of y = 4x2 is a reflection of y = –4x2 across the
y-axis.
Problem #5
Obj 5 - TAKS th [A.D1(B)]

6. Which expression is equivalent to ?B C D
Problem #6
Obj 5 - TAKS th [A.D3(A)]

7. What are the roots of the function graphed to the right?
A (–1, –9) and (0, –8)
B (0, –4) and (2, 0)
C (–4, 0) and (2, 0)
D (0, 2) and (0, –4)
Problem #7
Obj 5 - TAKS th [A.D2(B)]

8. How does the graph of y = x2 differ from the graph of y = x2 – 4?
A The graph of y = x2 – 4 is wider than the graph of y = x2.
B The graph of y = x2 – 4 is shifted to the left of the graph
y = x2.
C The graph of y = x2 – 4 is shifted down from the graph of
D The graph of y = x2 – 4 is narrower than the graph of y = x2.
Problem #8
Obj 5 - TAKS th [A.D1(C)]

9. A The rocket reached its maximum height after 2.5 seconds.
The graph to the right shows h, the height in meters of a model rocket, versus t, the time in seconds after the rocket is launched. From the graph, what conclusion can be made about the flight of the rocket?
A The rocket reached its maximum height after 2.5 seconds.
B At 0 seconds the rocket was 2 meters off the ground.
C The height of the rocket was 0 meters when it was launched.
D The rocket was in flight for 5 seconds.
Problem #9
Obj 5 - TAKS th [A.D1(D)]

10. The graph to the right shows the height of a baseball from the time it is thrown from the top of a building to the time it hits the ground.
How much time elapses while the baseball is 80 meters or more above the ground?
A 1 sec
B 9 sec
C 7 sec
D 6 sec
Problem #10
Obj 5 - TAKS th [A.D1(D)]

11. The completion of a certain chemical reaction is expressed by the equation y = 250 – 5x – x2, where y is the number of seconds needed to complete the reaction and x is the temperature in degrees Celsius at which the reaction occurs. If the reaction is complete in 200 seconds, what is the temperature at which the reaction occurs?
A 5°C
B 7°C
C 10°C
D 12°C
Problem #11
Obj 5 - TAKS th [A.D2(A)]

12. Which ordered pair represents one of the roots of the function f(x) = 2x2 + 3x – 20?
B (-4, 0)
C (–5, 0)
D (–20, 0)
Problem #12
Obj 5 - TAKS th [A.D2(B)]

13. The area of a rectangle is 144j9k15 square units
The area of a rectangle is 144j9k15 square units. If the width of the rectangle is 8j4k5 units, what is the rectangle’s length?
A j13k20 units
B 152 j13k20 units
C 136j5k10 units
D 18j5k10units
Problem #13
Obj 5 - TAKS th [A.D3(A)]

14. Which equation will produce the widest parabola when graphed?
A y = 2x2
B y = –6x2
C y = –0.6x2
D y = 0.2x2
Problem #14
Obj 5 - TAKS th [A.D1(B)]

15. In the graph of the function y = x2 + 5, which describes the shift in the vertex of the parabola if, in the function, 5 is changed to –2?
A. 3 units up
B. 7 units up
C. 3 units down
D. 7 units down
Problem #15
Obj 5 - TAKS th [A.D1(C)]

16. Which expression describes the area in square units of a rectangle that has a width of 4x3y2 and a length of 3x2y3?
A. 12x6y6
B. 12x5y5
C. 7x6y6
D. 7x5y5
Problem #16
Obj 5 - TAKS th [A.D3(A)]

17. The area of a rectangle is 30m11n5 square units
The area of a rectangle is 30m11n5 square units. If the length of the rectangle is 6m4n2 units, how many units wide is the rectangle? (m ≠ 0 and n≠ 0)
A. 5m7n3 units
B. 24m7n3 units
C. 36m15n7 units
D. 180m15n7 units
Problem #17
Obj 5 - TAKS th [A.D3(A)]

18. When graphed, which function would appear to be shifted 2 units up from the graph of f(x) = x2 + 1?
A. g(x) = x2 – 1
B. g(x) = x2 + 3
C. g(x) = x2 – 2
D. g(x) = x2 + 2
Problem #18
Obj 5 - TAKS th [A.D1(C)]

19. B. Sales gradually increased, reached a peak, and then leveled off.
The sales record for a recent hit CD at Tony’s Music Store is shown on the graph to the right. Which statement best describes the sales of this CD?
A. Sales rapidly increased, reached a peak, and then gradually decreased.
B. Sales gradually increased, reached a peak, and then leveled off.
C. Sales rapidly increased, reached a peak, and then rapidly decreased.
D. Sales remained constant throughout the time period.
Problem #19
Obj 5 - TAKS th [A.D1(D)]

20. The graph of the function
y = x2 is given to the right. How will the graph be affected if the coefficient of x2 is decreased to ¼?
A. The parabola will be wider.
B. The parabola will be narrower.
C. The parabola will be translated up.
D. The parabola will be translated down.
Problem #20
Obj 5 - TAKS th [A.,D1(B)]

21. What are the roots of the quadratic equation x2 – 3x + 2 = 0?
A. –2 and –1
B. –2 and 1
C. 2 and –1
D. 2 and 1
Problem #21
Obj 5 - TAKS th [A.D2(B)]

22. The polynomial x2 + x – 6 is modeled below using algebraic tiles.
What are the solutions to the equation x2 + x = 6?
A. x = –3 and x = –2
B. x = –3 and x = 2
C. x = 3 and x = –2
D. x = 3 and x = 2
Problem #22
Obj 5 - TAKS th [A.D2(A)]

23. The area of a rectangle is 144a8b4 square units
The area of a rectangle is 144a8b4 square units. If the width of the rectangle is 8a2b2 units, what is the length in units?
A. 18a6b2 units
B. 136a6b2 units
C. 152a10b6 units
D. 1152a10b6 units
Problem #23
Obj 5 - TAKS th [A.D3(A)]

24. A. The slope of the graph changes.
What is the effect on the graph of the equation y = x2 + 1 when it is changed to y = x2 + 5?
A. The slope of the graph changes.
B. The curve translates in the positive x direction.
C. The graph is congruent, and the vertex of the graph moves up the y-axis.
D. The graph narrows.
Problem #24
Obj 5 - TAKS th [A.D1(C)]

25. What are the x-intercepts of the graph of the equation y = x2 + x – 12?
A. x = 4, x = 3
B. x = –4, x = 3
C. x = –4, x = –3
D. x = 4, y = –3
Problem #25
Obj 5 - TAKS th [A.D2(B)]

26. What is the solution set for the equation 4(3x – 2)2 = 36? A.B. C. D.
Problem #26
Obj 5 - TAKS th [A.D2(A)]

27. Which expression best represents the simplification of
(3m–2n4)(–4m6n–7)? A. B. C. D.
Problem #27
Obj 5 - TAKS th [A.D3(A)]

28. Which shows the functions correctly listed in order from widest to narrowest graph?B. C. D.
Problem #28
Obj 5 - TAKS th [A.D1(B)]

29. The graph of a function is shown below.
If the graph is translated 7 units down, which of the following best represents the resulting graph?
Problem #29
Obj 5 - TAKS th [A.D1(C)]

30. Problem #29
Obj 5 - TAKS th [A.D1(C)]

31. Which expression represents the area of a rectangle with
sides measuring 2x2 y4 z units and 5xy4 z3 units?
7x2 y8 z3 units2
7x3 y8 z4 units2
10x3 y8 z4 units2
J. 10x2 y8 z3 units2
Problem #30
Obj 5 - TAKS th [A.D3(A)]

32. The graph of the function y = x2 − 3 is shown below.
If the graph of the original function is shifted 5 units up, which of the following equations best represents the translation of each point on the curve?
F. y = x2 + 5
G. y = x2 + 2
H. y = x2 − 2
J. y = x2 − 8
Problem #31
Obj 5 - TAKS th [A.D1(C)]

33. What is the simplified form of ?B. C. D.
Problem #32
Obj 5 - TAKS th [A.D3(A)]

34. Shirley graphed a function of the form y = ax2 + c. She then
translated the graph 8 units up, resulting in the function
y = - ⅔ x Which of the following best represents Shirley’s original function?
Problem #33
Obj 5 - TAKS th [A.D1(C)]

35. According to the graph, which time interval
An object was dropped from a height of 250 meters and fell to the ground. The graph below shows the change in h, the object’s height in meters, with respect to t, the time in seconds.
According to the graph, which time interval
best represents when the object was at 140 meters above the ground?
F. Between 3 seconds and 3.25 seconds
G. Between 3.75 seconds and 4 seconds
H. Between 3.5 seconds and 3.75 seconds
J. Between 3.25 seconds and 3.5 seconds
Problem #34
Obj 5 - TAKS th [A.D1(D)]

36. Which lists the functions of the form in order
from the widest to the narrowest graph?
Problem #35
Obj 5 - TAKS th [A.D1(B)]

37. Which graph best represents an equation that has the roots x = and
Problem #36
Obj 5 - TAKS th [A.D2(B)]

38. Marlena was asked to find an expression that is not equivalent to 212
Marlena was asked to find an expression that is not equivalent to Which of the following is not equivalent to the given expression?
F. (2 )
G. (28 )4
H. (26 )(26 )
J. (23 )(29 ) 2 6
Problem #37
Obj 5 - TAKS th [A.D3(A)]

39. The graph of a function of the form y = ax2 + c is shown below.
If the graph is translated only
up or down to include the
ordered pair (6, 7), which of
the following equations best
represents the resulting
graph?
Problem #38
Obj 5 - TAKS th [A.D1(C)]

40. What is the simplified form of ?G. H.
J. −
Problem #39
Obj 5 - TAKS th [A.D3(A)]

41. Which points best represent the roots of the graphed quadratic equation shown below?
F. (6 ½ , 0) and (4 ½ , 6)
(4 ½ , 6) and (2 ½ , 0)
H. (2 ½ , 0) and (6 ½ , 0)
J. (0, 2 ½ ) and (0, 6 ½ )
Problem #40
Obj 5 - TAKS th [A.D2(B)]

42. Which of the following is the vertex of the graph of the
equation y = −x2 + 2x + 3?
A. (0, 3)
B. (−1, 0)
C. (1, 4)
D. (3, 0)
Problem #41
Obj 5 - TAKS th [A.D1(D)]

43. How does the graph of y = − ¾ x2 differ from the graph of y = x2 ?
The graph of y = − ¾ x2 opens downward and is
wider than the graph of y = x2 .
G. The graph of y = − x2 opens upward and is
wider than the graph of y = ¾ x2 .
H. The graph of y = − x2 opens upward and is
narrower than the graph of y = ¾ x2 .
J. The graph of y = − x2 opens downward and is
Problem #42
Obj 5 - TAKS th [A.D1(B)]