Expert: Alon Mandes - 3/20/2010

Question
Please help!

1. 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


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

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


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


4. 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

5. 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

Answer
1. f(x) = 4(x - 3)^2 - 2
  This function have a Domain of : all x
  The Range is : y ≥ -2 . "Beause the smallest value of 4(x-3)^2 is 0
2. (3y-4)/5=(y+1)/2 --> 2(3y-4)=5(y+1) --> 6y-8=5y+5 --> 6y-5y=5+8 --> y=13 .
3. 2(3√x)+9=5 --> 6√x=-4 --> (6√x)²=(-4)² --> 36x=16 --> 9x=4 --> x=4/9 .
4. The roots are x1=-3 AND x2=1 . Therefore : (x-x1)(x-x2)=0 --> (x-[-3])(x-1)=0 -->
  (x+3)(x-1)=0 --> x²+3x-x-3=0 --> x²+2x-3=0 .
5. The roots are x1=3/2 AND x2=-1/2 . Therefore : (x-x1)(x-x2)=0 --> (x- 3/2)(x+ 1/2)=0
  --> x² - 3x/2 + x/2 - 3/4 =0 -->  x²-x-(3/4)=0 --> 4x²-4x-3=0 .

Alon.