Answer Page!!
  
1)   Midpoint is (3, 2)
 

2)  x + y = 5
    2x - y = 1
      3x = 6
        x = 2
Thus the intersection point is (2, 3)


 
3)  a)  m = (3 + 3)/(5 - 2) = 6/3 = 2
 
     b)  4x + 5y = 10
                  5y = -4x + 10
                    y = (-4/5)x + 2
           m = -4/5
 
     c)  y = -5 is a horizontal line, thus the slope is zero.

 
4)  Slope for first line is (2 + 3)/(7 - 2) = 5/5 = 1
     Slope for the second line is (7 - 2)/(-3 - 2) = 5/(-5) = -1
     Thus, they are perpendicular because the slopes are negative reciprocals.

 
5)  a)  Use intercept form:  x/2 + y /-3 = 1      Multiply by 6.
                                          3x - 2y = 6
 
     b)  Use point - slope form.  Find slope.  It is 1.  Use one of the points.
                                   y - 5 = x - 1
                                   -x + y - 5 = -1
                                   -x + y = 4 or x - y = -4
 
     c)  Find the slope of x + 3y = 6
                                           3y = -x + 6
                                             y = (-1/3)x + 2
                                          The slope is -1/3 Since the line we want is parallel to this line, it has the same slope.  (0, 0) is the y-intercept.  Use the slope-intercept form.
                                                 y = (-1/3)x + 0
                                                3y = -x
                                                x + 3y = 0

 
6)  a)  The fixed cost is 290 and the variable cost is .25m.  Thus the equation is C(m) = .25m + 290
 
     b)  The slope is .25
 
     c)  C(1200) = .25(1200) + 290 = 300 + 290 = 590.    $590

 
7) 

 
8)  a)  (3x - 2)(x + 4) = 24
            3x2 + 10x - 8 = 24
            3x2 + 10x - 32 = 0
            (x - 2)(3x + 16) = 0
               x = 2, x = -16/3
 
     b)  2x2 - 4x = -5
            x2 - 2x = -5/2
          x2 - 2x + 1 = -3/2
          (x - 1)2 = -3/2
            x - 1 = 

     c) 

 
 
9)  Vertex point is at -b/2a = -2/2 = -1  Substitute into the equation to find the y value
        1 - 2 - 15 = -16   Thus, the vertex point is (-1, -16)
 
     Axis of symmetry is the vertical line through the vertex point.  x = -1
 
     y-intercept is (0, -15)
 
     x-intercepts are found by finding the zeroes of the function
                    x2 + 2x - 15 = 0
                     (x + 5)(x - 3) = 0
                     intercepts are:  (-5, 0) and (3, 0)


 
10)  y = 4x2 + 8x + 2
     y = 4(x2 + 2x     ) + 2
     y = 4(x2 + 2x + 1) +2 - 4
     y = 4(x + 1)2 - 2
      The vertex point is (-1, -2)

 
11)  a)  f(40) = 40 + 1600/25 = 104 ft
 
      b)  f(50) = 50 + 2500/25 = 150 ft
 
      c)  46 ft.
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