Order of transformations:

1. Replace x by -x (reflects graph across y-axis)
2. Replace x by x±k (shifts graph k units horizontally, 
   left if x-k, and right if x+k)  
3. Multiply right side by a positive number k
   Stretches vertically by factor of k if k>1
   Shrinks vertically by a factor of k if k<1  
4. Multiply right side by -1 (reflects graph across the x-axis) 
5. Add to or subtract from the right side (shifts graph up if
   adding a positive number, and down if adding a negative.) 


a.)  y = 3x^2 - 8

transformation              effect on graph:

 y = x^2             <--- original equation, has vertex (0,0)
                          axis of symmetry x=0 
                         

                          Multiplying right side by 3, which is >1,
 y = 3x^2            <--- stretches vertically by factor of 3, still
                          has vertex (0,0), axis of symmetry x=0
                                  

                          Subtracting 8 from right side
 y = 3x^2 - 8        <--- shift 8 units downward, vertex (0,-9) 
                          axis of symmetry x=0

===========================================================

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

transformation              effect on graph:

y = x^2               <--- original equation, has vertex (0,0)
                           axis of symmetry x=0 
 
                           Replacing x by (x-6)
 y = (x-6)^2          <--- shifts 6 units right, has vertex (6,0)
                           axis of symmetry x=6                           

                           Adding 4 to right side
 y = (x-6)^2 + 4      <--- shifts 4 units upward, vertex (6,4) 
                           axis of symmetry x=6
 
============================================

c.)  y = -4(x + 3)^2 - 7 

transformation              effect on graph:

y = x^2               <--- original equation, has vertex (0,0)
                           axis of symmetry x=0 
 
                           Replacing x by (x+3)
 y = (x+3)^2          <--- shifts 3 units left, has vertex (-3,0)
                           axis of symmetry x=-3                           

                           Multiplying right side by 4, which is >1,
 y = 4(x+3)^2         <--- stretches vertically by factor of 4, still
                           has vertex (-3,0), axis of symmetry x=-3
                           
                           Multiplying right side by -1
 y = -4(x+3)^2        <--- reflects across x-axis, vertex (-3,0)
                           axis of symmetry x=-3

                           Subtracting 7 from right side
 y = -4(x+3)^2 - 7    <--- shift 7 units downward, vertex (3,-7) 
                           axis of symmetry x=-3
 
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Edwin