algebra questions

–when a number or variable is squared: axsquared is a times x squared

(ax)squared is ax squared

For which quadratic function is −3 the constant term?

a. y=(3x+1)(−x–3)

b. y=x2–3x+3
c. f(x)=(x–3)(x–3)

d. y=−3x2 +3x+9

2. The vertex of a parabola is (3, 2). A second point on the parabola is (1, 7). Which point is also on the parabola?

a. (−1, 7)

b. (3, 7)

c. (5, 7)

d. (3, −2)

3. The graph of a quadratic function has vertex (−3, −2). What is the axis of symmetry?

a. x = –3

b. x = 3

c. y=−2

d. y = 2

4. Which function is not a quadratic function?

a. y=(x–1)(x–2)

b. y=x2+2x–3
c. y=3x–x2

d. y=−x2 +x(x–3)

What is the vertex of y=−2x to the second power –4x–5?

a. (−2, −3)

b. (1, −3)

c. (1, −11)

d. (−1, −3)

6. What is the y-intercept of y = (x + 1)to the second power – 2?

a. (0, −1)

b. (0, −3)

c. (0, 1)

d. (0, −2)

7. The bottom of a box is to be a rectangle with a perimeter of 36 cm. The box must be 4 cm high. What dimensions give the maximum volume?

a. l=14cm,w=4cm

b. l=9cm,w=9cm

c. l=12cm,w=6cm

d. l=8cm,w=10cm

8. The bottom of a box is to be a rectangle with a perimeter of 36 cm. The box must be 4 cm high. What is the maximum volume?

a. 324 cm cubed

b. 320 cm cubed

c. 288 cm cubed

d. 224 cm cubed

9. The vertex of the graph of y = −xsquared – 16x – 62 lies in which quadrant?

a. IV

b. III

c. II

d. I

Use the following information about quadratic functions to answer questions 11 – 16

vertex form: y=a(x–h)squared +k

standard form: y=axsquared +bx+c

11. When y = −3xsquared – 18x – 23 is written in vertex form, what is the value of k?

a. 4
b. −3

c. 54

d. −18

12. When y = 2(x – 3)(x + 5) is written in standard form, what is the value of b?

a. 2

b. 4
c. −30

d. 5

13. When y = −2(x + 3)squared + 25 is written in standard form, what is the value of c?

a. 2

b. 18

c. 12

d. 7

14. For y = −3xsquared – 7x + 5, what is the x-value of the vertex?

a . − 53

b. 73

c. −76

d. 56
15. What is the y-coordinate of the vertex of y = −2(x + 1)squared + 3?

a. −2

b. 1

c. 3

d. 2

16. How many units down must you shift the graph of y = 3(x + 3)squared to get the graph of y=3(x+3)squared –2?

a. 2

b. 3

c. 9

d. 6

17. Which term is not a common factor of 4a squared c squared + 2a squared c – 6ac squared?

a. 4c

b. 2a

c. 2ac

d. ac

18. How can you write (m – 5)(m + 4) + 8 as a product of two binomials?

a. (m–1)(m+8)

b. (m–4)(m+3)
c. (m+8)(m+8)
d. (m–5)(8m+32)

19. What is the factored form of 4xsquared + 15x – 4?

a. (2x+2)(2x–2)

b. (2x–4)(2x+1)

c. (4x+1)(x–4)

d. (4x–1)(x+4)

20. Which is a factored form of 0.81psquared – 0.09?

a. (0.9p + 0.045)(0.9p – 0.045)

b. (0.09p + 0.03)(0.09p – 0.03)

c. (0.9p + 0.3)(0.9p – 0.3)
d. (0.9p + 0.81)(0.9p – 0.81)

21. The period of a pendulum is the time the pendulum takes to swing back and forth one full time. The function I = 0.81t squared relates the length l in feet of a pendulum to the time t in seconds that it takes to swing back and forth. The convention center in Portland, Oregon, has the longest pendulum in the U.S. The pendulum’s length is 90 ft. Find the period for this pendulum.

a. 8.5 seconds

b. 10.5 seconds

c. 90 seconds

d. 111 seconds

22. What are the values of x that satisfy the equation 3 – 27xsquared = 0?

a. x = ± 3

b . x = ± 31
c. x= 91 or x=−91

d. x=2 square root 6 or x=−2 square root 6

23. What are the solutions of the equation 6x squared + 9x – 15 = 0?

a. 1, −15

b. 1,−52

c. −1, −5

d. 3, 52

24. For which equation is −3 not a solution?

a. xsquared –2x–15=0

b. xsquared–21=4x
c. 2xsquared +12x=−18

d. 9+xsquared=0

25. What are the solutions of the equation (2x – 7)squared = 25?

a. 6, −6

b. 6, 1
c. 6,−1

d. −6, −1

26. Find the sum of the solutions to the equation x squared + 2x – 15 = 0.

a. 8

b. −8

c. 2

d. −2

27. Find the product of the solutions to the equation x squared – 8x = 9.

a. 6

b. −6

c. 9

d. −9

28. Which equation has − 2/5 as a solution?

a. (2x–5)(x+1)=0

b. (2x+5)(x+1)=0

c. (5x–2)(x+1)=0

d. (5x+2)(x+1)=0

29. How many times does the graph of y = xsquared – 4x – 5 cross the x-axis?

a. 0

b. 1

c. 2

d. 33

30. The equation xsquared – 3x + a = 0 has two roots. One root of the equation is 2. What is the other root?

a. −2

b. −1

c. 1

d. 3

31. What is the number square root -225 + 36 when written in the form a + bi? (square root is ONLY for -225)

a. −15+6i

b. 6+15i

c. 6–15i

d. 36 + 15i

32. How can you rewrite the expression (8 – 5i)squared in the form a + bi?

a. 39 + 80i

b. 39 – 80i

c. 69+80i

d. 69 – 80i

33. What are the solutions of −4xsquared – 72 = 0?

a. ±2i square root 3

b. ±3i square root 2

c. ±2 square root 3

d. ±3 square root 2

34. Which description of the graph of y = axsquared + bx + c is not possible?

a. There are two x-intercepts, the vertex is below the x-axis, and a > 0.

b. There is one x-intercept and the vertex is on the x-axis.
c. There are two x-intercepts, the vertex is below the x-axis, and a < 0.

d. There are no x-intercepts, the vertex is above the x-axis, and a > 0.

35. What can you add to xsquared + 5x + ___ to get a perfect square trinomial?

a. 5
b. 6.25

c. 25

d. 2.5x

36. How can you rewrite the equation xsquared + 12x + 5 = 3 so the left side of the equation is in the form (x – a)squared?

a. (x–6)2=28

b. (x+6)2=34

c. (x+6)2=39

d. (x+12)2 =−2

37. What is the discriminant of qx squared + rx + s = 0?

a. |a+b|

b. q squared – 4rs

c. r squared – 4qs

d. s squared – 4qr

38. How many different real solutions are there for 2x squared – 3x + 5 = 0?

a. 0

b. 1

c. 2

d. i

39. Which equation has −3 + 5i as its solutions?

a. x squared +6x=−34

b. x squared+6x=−14

c. x squared+3x=4
d. x squared+3x=2

40. If a quadratic equation has a discriminant that equals zero, which of the following statements is always true?

a. The equation has two solutions and the parabola will open upward.
b. The equation has one solution and the parabola will open downward.
c. The equation has zero solutions and there is not enough information to determine the direction of the parabola.

d. The equation has one solution and there is not enough information to determine the direction of the parabola.

43. Write the equation of a parabola with vertex (−3, −4) in vertex form.

a. y=(x–3)squared +4

b. y=2(x–5)squared +2

c. y=(x+3)squared –4

d. y=(x+5)squared –2

44. Factor 4x squared + 5x – 21.

a. (4x–7)(x+3)

b. (4x+7)(x–3)

c. (x+3)(4x+7)

d. (4x–7)(x–3)

45. Factor x squared – 15x + 54.

a. (x–3)(x–18)

b. (x+1)(x+54)

c. (x+9)(x+6)

d. (x–9)(x–6)

46. Solve 6x squared = 48; round your answer to the nearest hundredth.

a. ± 6.93
b. ± 2.83
c. ± 16.97
d. none of these

47. Simplify (−5 – 4i)(2 + 9i).

a. 26 – 37i

b. −46–53i

c. −46–37i

d. 26 – 53i

48. Simplify (3 + 3i) – (7 + 6i).

a. −4–3i

b. 4 – 3i

c. 4+3i

d. −4+9i

49. What can you add to x squared + 6x + ___ to get a perfect square trinomial?

a. 3

b. 12

c. 9

d. 6

50. Without graphing, tell how many x-intercepts does the graph y = −3x squared + 4x + 4 have?

a. 3 intercepts

b. 2 intercepts

c. 1 intercepts

d. 0 intercepts