Expert: Richard J. Raridon - 5/14/2010

Question
Determine the vertex coordinates for:  f(x) = 3x^2 - 5x - 2

a)( 1 , -49/12 )  
b)( 5/6 , -49/12 )  
c)( 5/6 , 1/12 )
d)(-1,-7)

2. Determine the vertex coordinates for:  h(x) = (2x - 5)(2x + 3)

a)( 1/2 , -16 )  
b)( -1/2 , -16 )
c)( 1/4 , 14 )
d)(-2, -16)

3. Determine the vertex coordinates for: f(x) = 9 - 8x - x2

a)(-4,5)  
b)(4,25)
c)(-4,25)  
d)(5,-4)

4. Determine the vertex coordinates for: g(x) = (6 + x)(4 + x)

a)( -5/2 , 1 )
b)( 1/2 , -5 )
c)(4,-1)  
d)( -5 , -1 )


5. Determine the vertex coordinates for: f(x) = 2(x - 5)2 - 8

a)(5,-8)  
b)(-5,8)
c)(-8,5)  
d)(8,-5)

6. Determine the domain for: f(x) = 9 - 8x - x^2
a) D = {y ≤ 25}  
b)D = {all reals}
c)D = {y ≥ 25}  
d)D = {y < 25}

7. Determine the domain for:
g(x) = (6 + x)(4 + x)

a)D = {y ≥ -0.5}  
b)D = {all reals}
c)D = {y ≥ 0.5}
d)D = ø

8. Determine the domain for:  f(x) = 2(x - 5)^2 - 8

a)D = {x ≥ -8}  
b)D = {3,7}
c)D = {all reals}  
d)D = {-8}

9. Determine the range for: f(x) = 9 - 8x - x^2

a)R = {y ≥ 25}  
B)R = {y ≤ 25}
c)R = {all reals}  
d)R = ø

10. Determine the range for:  g(x) = (6 + x)(4 + x)

a)R = {y ≥ -1}  
b)R = {all reals}
c)R = {y ≥ -5}  
d)R = ø

11. Determine the range for:  f(x) = 2(x - 5)^2 - 8

a)R = {y ≥ -8}  
b)R = {y ≥ 5}
c)R = {all reals}  
d)R = ø

12. Determine the range for:
f(x) = 9 - 8x - x^2

a)R = {y ≥ 25}  
b)R = {y ≤ 25}
c)R = {all reals}  
d)R = ø

13. Determine the range for:  
g(x) = 1/2(6 + x)(4 + x)

a)R = {y ≥ -1/2}  
b)R = {all reals}
c)R = {-6,-4}  
d)R = {y ≤ -1/2}

14. Determine the range for:  
f(x) = 4(x - 3)^2 - 2

a)R = {y ≥ -2}  
b)R = {y ≤ 3}
c)R = {all reals}  
d)R = ø

15. Solve:  15-2n = n^2

a)-3 or 5  
b)15 or -1
c)3 or -5  
d)0 or 3

16. Solve: 3y - 4/5 = y + 1/2

a)13/11
b) -3 / 11
c)-11/3
d)13


17. Solve:  2 · 3  √ x + 9 = 5
a)-2  
b)-8
c)-6  
d)No solution

18. Solve:   5|n|-7 = 3

a)5 or -5  
b)2 or -2
c).5 or -.5  
d)No solution

19. Determine the quadratic equation with integral coefficients having the roots: -3 and 1

a)x^2 + 2x + 3 = 0  
b)x^2 - x - 3 = 0
c)x^2 + 2x - 3 = 0  
d)x^2 - 2x + 3 = 0

20. Determine the quadratic equation with integral coefficients having the roots:  3/2 and -1/2

a)4x^2 - 4x - 3 = 0  
b)4x^2 + 4x + 3 = 0
c)4x^2 - 8x - 3 = 0
d)4x^2 + 8x - 3 = 0

21. Determine the quadratic equation with integral coefficients having the roots:   2 + √ 7  and 2 - √ 7  

a)x^2 - 4x - 3 = 0  
b)x^2 + x + 2 = 0
c)x^2 + x - 2 = 0  
d)x^2 + 4x - 3 = 0

22. Determine the quadratic equation for the parabola:  maximum value: 6;  x-intercepts: -2 and 4

a)f(x) = -2x^2 + 4x + 16  
b)f(x) = .67x^2 + 1.33x - 5.33
c)f(x) = 2x^2 - 4x + 16  
d)f(x) = -.67x^2 + 1.33x + 5.33

23. Determine the quadratic equation for the parabola: minimum value: -5;  x-intercepts: -2 and 3

a)f(x) = -4x^2 + 4x + 24  
b)f(x) = 4x^2 - 4x - 24
c)f(x) = 5x^2 - 4x - 24  
d)f(x) = 4/5x^2 - 4/5x - 24/5

24. Determine the quadratic equation for the parabola:  vertex: (-1,-10);  x-intercepts: -6 and 4

a)f(x) = 4/5x^2 + 2/5x - 48/5  
b)f(x) = 2x^2 + 4x - 48
c)f(x) = 2/5x^2 + 4/5x - 48/5  
d)f(x) = 5x^2 + 4x - 48

25. Determine the quadratic equation for the parabola:  maximum value: 9;  zeros of  f: -6 and 0

a)f(x) = x^2 - 6x  
b)f(x) = -x^2 - 6x
c)f(x) = -x^2 - 9x  
d)f(x) = x^2 - 6

26. Determine the quadratic equation for the parabola: minimum value: -4 when x = 3;  zeros of  f: one is 6

a)f(x) = -4/9x^2 + 8/3  
b)f(x) = 4/9x^2 - 8/3x
c)f(x) = 4/9x^2 + 8/3x  
d)f(x) = -4/9x^2 - 8

27. Determine the quadratic equation for the parabola:  
range: {y:y ≤ 9};  x-intercepts: -2 and 4

a)f(x) = x^2 - 2x + 8  
b)f(x) = x^2 + 2x - 8
c)f(x) = -x^2 + 2x + 8  
d)f(x) = -x^2 - 2x + 8

28. Find two numbers such that their sum is 20 and the sum of their squares is as small as possible.
a)10 + 10  
b)5 + 15
c)0 + 20 d)no solution

29. A rectangular pen is made with 100 m of fencing in three sides. The fourth is a stone wall. Find the greatest possible area of such an enclosure.
a)1667 m^2  
b)1250 m^2
c)5000 m^2  
d)1600 m^2

30. A ferry service transporting passengers to an island charges a fare of $10 and carries 300 persons. The manager estimates that the company will lose 15 passengers for each increase in fare of $1. Find the fare that yields the greatest income.
a)$16  
b)$16.50
c)$18  
d)$15

31. A ball is thrown vertically upward from the ground with an initial speed of 80 ft/sec. Its height is given by h = 80t - 16t2. How high does the ball go? When does the ball hit the
a)100 ft;  5 sec  
b)457 ft;  10 sec
c)320 ft;  5 sec  
d)150 ft;  10 sec

32. Find the maximum value of the function:y = -x^2 + 8x - 4
a)8  
b)22
c)16  
d)12

33. Determine whether the following has a maximum or minimum value and then compute that value: y = 2x^2 + 10x - 4

a)minimum;  16.5  
b)maximum;  16.5
c)minimum;  -16  
d)minimum;  -16.5

Part 2
Type the answer to the problem in the text box below each item. Be sure legibly show all work in your notebook. Remember to include any applicable units. If there is no solution, type "no solution". If there is not enough information present to solve the problem, type "not enough information". (Each question is worth one point)

34. Find the min/max and vertex of the function
g(x) = 2x2 + 8x


35. Find the min/max and vertex of the function:
h(x) = (2x - 5)(5 + x)


36. Find the min/max and vertex of the function:
g(x) = 2x^2 - 6x^2 + 2


37. Find a quadratic equation with integral coefficients having the given roots:
4 + 2i, 4 - 2i


38. Find a quadratic equation with integral coefficients having the given roots i√ 5 , -i√ 5

Answer
1. b
2. a
3. c
4. d
5. a
6-14.  They didn't teach ranges and domains when I took algebra 60 years ago
15. c
16. none of those, y = 13/20
17. ?
18. b
19. c
20. a
21. a
22. c
23. b
24. b
25. a
26. b.
27. c
28. a
29. b
30. d
31. a
32. d
33. d
34. (-2,-8)
35. (-5/4, -225/8)
36. ?
37. x^2-8x+20 = 0
38. x^2+5 = 0