Expert: Richard J. Raridon - 8/4/2010

Question
2. Solve:
2x^4 + 7x^2 - 4 = 0

0.5
± √ 2/2 or ± 2i
1
2i

3. Solve:
(x^2 + 3)^2 - 6(x^2 + 3) = 7


±2 or ±2i
√ 2  or √ 10  
±4
±2 or no solution

4. Solve: 3/n - 7/n^.5 - 6 = 0
1/3
1/9
2/3
9

5. Solve: 2t + 3 = 5√ t
-4.5 or -1
1 or 2.25
1.33 or 3
-1 or 3

6. Solve: 2/x - 5/x = 1
3
1.67
-0.67
-3

7. Simplify: 3 · √ -384
12i√ 24

6i√ 96
24i√ 6  
72i

8. For what values of x is the following true? √ (x-4)^2 = 4 - x
7/5
x = 4
x = 2
x </= 4


10. Simplify:
The cube root of 250 minus the cube root of 128 plus the cube root of 16.

4(^3  √ 2)
10√ 3
3(^3  √ 2 )
3√ 2


11. Simplify: (2√ 3 + 5)(4√ 3 - 3)  
14(√ 3 ) + 9
2√ 2
3
8 - 12√ 3


12. Solve: 2√  x + 3 = x
1
9
16(^3  √ 5 )
 14√ 6


13. Choose the correct vertex for the equation:
y + 1 = 0.5x^2

(0,-1)  (0,1)
(1,0)  (-1,0)

14. Choose the correct vertex for the equation:
y - 5 = - (x + 2)^2

(2,5)  (5,-2)
(-2,-5)  (-2,5)

15. Find an equation y - k = a(x - h)^2 for the parabola described:
vertex:  (4,5);  contains:  (5,3)

y - 5 = 2(x - 4)^2
y - 5 = -2(x - 4)^2
y + 5 = -2(x - 4)^2
y + 5 = 2(x + 4)^2

16. Find an equation y - k = a(x - h)^2 for the parabola described:
vertex:  (-3,6);  x-intercept:  contains the origin

y - 6 = -0.67(x + 3)^2
y + 6 = -0.67(x - 3)^2
y - 6 = 0.67(x + 3)^2
y + 6 = 2(x - 3)^2

17. Find an equation y - k = a(x - h)^2 for the parabola described:
vertex:  (-2,6);  y-intercept:  -2

y + 6 = 2(x + 2)^2
y - 6 = 2(x - 2)^2
y - 6 = -2(x + 2)^2
y + 6=-4(x - 2)^2

18. Find an equation y - k = a(x - h)^2 for the parabola described:  
vertex:  (-3,4);  x-intercept:  -1

y - 4 = 0
y + 4 = (x + 3)^2
y + 4 = -(x + 3)^2
y - 4 = -(x + 3)^2

19. If the parabola y - k = -3(x - 1)^2 passes through the origin, find k.
k = -3
k = -1
k = 0
k = 3

20. If the parabola y + 5 = a(x + 2)^2 has a y-intercept 4, find a.
a = 0.82
a = -5
a = 5
a = 2.25

21. Find values of a and k for a parabola containing the points given:  
y - k = a(x + 3)^2;  (-5,1) and (1,7)

a = 2; k = 3
k = .5 = 3;
k = -1 a = .5;
a = 2;  k = -1

22. Without solving the equation, determine the nature of its roots:  (Hint: find the discriminant, b^2 - 4ac)
-2y2 + y + 6 = 0

rational, real
rational, imaginary
irrational, real
irrational, imaginary

23. Without solving the equation, determine the nature of its roots:
y = 0.5x^2 - 6x + 3

rational, real
rational, imaginary
irrational, real
irrational, imaginary

24. Without solving the equation, determine the nature of its roots:  
x^2 = 21x - 110

rational, real
rational, imaginary
irrational, real
irrational, imaginary

25. Find the correct roots if there are any: √ (x + 4) = -3
4
-4
No roots
0

26. Locate each real zero as an integer or between consecutive integers:  
y = x^2 + 4x - 4

between 0 and 2
3
between -5 and -4, and between 0 and 1
between -1 and 3, and between 2 and 6

27. Solve: y2-2y=99
-9
11
-9, 11
9, -11

30. Solve:
x^2 + 14 = 0

± i√ 14
√ 14
± 2√ 7
7√ 2

31. Choose the correct vertex for the equation:  
y + 1 = 0.5x^2

(0,-1)  (0,1)
(1,0)  (-1,0)

32. Choose the correct vertex for the equation:
y - 5 = -(x + 2)2

(2,5)
(5,-2)
(-2,-5)
(-2,5)

33. Find an equation y - k = a(x - h)^2 for the parabola described:  
vertex:  (4,5);  contains:  (5,3)

y - 5 = 2(x -4)^2
y - 5 = -2(x - 4)^2
y + 5 = -2(x - 4)^2
y + 5 = 2(x + 4)^2

34. Find an equation y - k = a(x - h)^2 for the parabola described:  
vertex:  (-3,6);  x-intercept:  contains the origin

y - 6 = -0.67(x + 3)^2
y + 6 = -0.67(x - 3)^2
y - 6 = 0.67(x + 3)^2
y + 6 = 2(x - 3)^2

35. Find an equation y - k = a(x - h)^2 for the parabola described:
vertex:  (-2,6);  y-intercept:  -2

y + 6 = 2(x + 2)^2
y - 6 = 2(x - 2)^2
y - 6 = -2(x + 2)^2
y + 6 = -4(x - 2)^2

Answer
6. -3
7. 24i(6)^1/2
9. x=4
10. 3(2^1/3)
11. 9+14(3^1/2)
12. 9
13. 0,-1
14. -2,5
15. y-5 = -(x-4)^2
16. y-6 = -0.67(x+3)^2
17. y-6 = -2(x+2)^2
18-21 too many alike
22. rational, real
23. irrational, real
24. irrational, real
25. no roots
26. between -1&3 and between 2&6
27. (-9,11)
30. +/-i(14^1/2)
31. 0, -1
32. same as 14
33. same as 15
34. same as 16
35. same as 17