REFLECTION BOOK I

REVIEW QUESTIONS        DECEMBER

Reflection 4
 

1.     Graph the function defined by the equation:    d(x) = - 2/3 x + 1

         a.     Determine the x and y intercepts of this function.
         b.     Is this function increasing or decreasing?
         c.     Discuss the signs of this function.

 

2.     Graph the function defined by the equation:    f(x) = 0.5 (x + 4)2 - 3

         a.     Determine the x and y intercepts of this function.
         b.     Is this function increasing or decreasing?
         c.     Discuss the signs of this function.

 

3.     Graph the function defined by the equation:    f(x) = -2(x + 2)(x - 3)

         a.     Determine the x and y intercepts of this function.
         b.     Is this function increasing or decreasing?
         c.     Discuss the signs of this function.

 

4.     Determine all the properties of the function whose equation is: g(x) = 3(x - 1)2 - 4:
        domain,  range, extreme, intercepts, interval of increase and decrease, signs.

 

5.     The span of a bridge is supported by a concrete arch
         in the shape of a parabola given by the equation:
          H =  - 2/45 (x2 - 60 x)
         where H represents the height (in metres) above the river
         and x is the width of the river.

         a.     What is the maximum height H above the river?

         b.     How wide is the river?




6.     Solve the following quadratic equations using the method of your choice.         

        a.   3x2 = 192                               b.  6x2 = 21x                                  c.  2x2 + 7x - 4 = 0

 

ANSWERS REFLECTION 4
 
 
1.        a.  x-int. (3/2, 0)    y-int.  (0, 1) 

           b.  y increasing for all  x values

           c.  y > 0  for  x :  ]-oo, 3/2 [
                y < 0  for  x :  ] 3/2, +oo[ 

 
 
 

2.        a.  x-int. (-13/2, 0) and (-3/2, 0)     y-int.  (0, 5) 

           b.   y   decreasing for  x : ]-oo, - 4 [
                 y   increasing for  x :  ]- 4, +oo[

           c.  y > 0  for  x :  ]-oo, -13/2 [  U  ] -3/2, +oo[ 
                y < 0  for  x :  ] -13/2 ,  3/2[ 

 
 
 
3.        a.  x-int. (-2, 0) and (3, 0)     y-int.  (0, 12) 

          b.   y   increasing for  x : ]-oo, 1/2 [
                y   decreasing for  x :  ]1/2, +oo[

           c.  y < 0  for  x :  ]-oo, -2[  U  ] 3, +oo[ 
                y > 0  for  x :  ] -2 , 3[ 

 
 
 

4.        a.  x-int. (- 0.15  , 0) and (2.15  , 0)     y-int.  (0, 1)                           

           b.   y   decreasing for  x : ]-oo, 1 [
                 y   increasing for  x :  ]1, +oo[

           c.  y > 0  for  x :  ]-oo, - 0.15 [   U    ]2.15, +oo[ 
                y < 0  for  x :  ] - 0.15,  2.15  [

 
 
 
5.        Standard form:
           H =  - 2/45 (x - 30)2 + 40
                  
           a.  Maximum  H = 40 m

           b.  Width = 60 m