
                            Review of Curves.
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About 5O% of a typical calculus course deals with curve-sketching.  If you
don't know the properties of simple curves, you will have trouble with the
more involved ones!  The following are properties of the simple curves.


   The equation of a straight line with slope m, and y-intercept b is

                           y = mx + b .


   The equation of a straight line with slope m, passing through the
   point x = x  , y = y  ,  is
              °        °
                      y - y  = m(x - x ) .
                           °          °


   The straight lines  y = m x + b   and  y = m x + b   intersect
                            1     1            2     2
   at right angles if
                             m  m   =  -1  .
                              1  2



   The equation of a circle, radius r, center x = x , y = y , is
                                                   °       °
                             2           2     2
                     (x - x )  + (y - y )  =  r  .
                           °           °


   The equation of a parabola with axis parallel to the y-axis is

                               2
                         y = ax  + bx + c  .

   If a > O, the parabola opens upwards.
   If a < O, the parabola opens downwards.
   The vertex of the parabola is at x = -b/2a.


   The equation of a parabola which crosses the x-axis at x = a, x = b, is

                         y = c(x - a)(x - b)  .


   The equation of a parabola with axis parallel to the x-axis is

                               2
                         x = ay  + by + c  .

   If a > O, the parabola opens to the right.
   If a < O, the parabola opens to the left.



   The equation of a cubic is

                                3     2
                          y = ax  + bx  + cx + d  .

   If a > O, the cubic starts in the 3rd quadrant and ends in the 1st.
   If a < O, the cubic starts in the 2nd quadrant and ends in the 4th.


   The equation of a cubic which crosses the x-axis at x = a, x = b, x = c is

                          y = d(x - a)(x - b)(x - c) .



   Two curves,  y = f(x) and y = g(x), intersect at x = x  , if
                                                         °
                             f(x )  =  g(x )  .
                                °         °


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