document.write( "Question 280229: I'm not even sure if this is where I put this answer. I have graphed and done equations, how do I figure this out? Is it a matter of doing equation on graphing calculator and the difference?\r
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\n" ); document.write( "\n" ); document.write( "Describe the transformations from f(x) = x2 to the function f(x) = -4 – 3x2.
\n" ); document.write( " shift up 4 units and 3 units to the left
\n" ); document.write( " shift down 4 units and 3 units to the right
\n" ); document.write( " shift down 4 units, reflect about the x-axis, vertical stretch of 3
\n" ); document.write( " shift up 4 units, reflect about the x-axis, horizontal stretch of 3 \r
\n" ); document.write( "\n" ); document.write( "Thanks for anyone who helps!
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Algebra.Com's Answer #203721 by jsmallt9(3758)\"\" \"About 
You can put this solution on YOUR website!
\"f%28x%29+=+x%5E2\"
\n" ); document.write( "To avoid confusion I'm going to use a different name for the second function:
\n" ); document.write( "\"g%28x%29+=+-4+-+3x%5E2\"
\n" ); document.write( "Now I'll rewrite g(x) in a form which we can use to find the answer:
\n" ); document.write( "\"g%28x%29+=+%28-1%29%283%29x%5E2+%2B+%28-4%29\"
\n" ); document.write( "Since \"f%28x%29+=+x%5E2\", this becomes:
\n" ); document.write( "\"g%28x%29+=+%28-1%29%283%29%28f%28x%29%29+%2B+%28-4%29\"
\n" ); document.write( "Looking at g(x) in this way we can see what transformations are being applied to f(x) to turn it into g(x):
  • The multiplication of f(x) by 3 means a vertical stretch by a factor of 3.
  • The multiplication of f(x) by -1 means a vertical \"flip\" (i.e. a reflection in the x-axis)
  • The addition of -4 means a downward shift of 4 units.
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