document.write( "Question 1100203: What is the parent function and each individual transformation step for f(x)=-3x^2-5 \n" ); document.write( "
Algebra.Com's Answer #715245 by greenestamps(13203)\"\" \"About 
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The parent function is f(x) = x^2:

\n" ); document.write( "\"graph%28400%2C400%2C-4%2C4%2C-50%2C20%2Cx%5E2%29\"

\n" ); document.write( "The graph is then reflected about the x-axis: f(x) = -x^2:

\n" ); document.write( "\"graph%28400%2C400%2C-4%2C4%2C-50%2C20%2C-x%5E2%29\"

\n" ); document.write( "Next the graph is stretched vertically by a factor of 3: f(x) = -3x^2

\n" ); document.write( "\"graph%28400%2C400%2C-4%2C4%2C-50%2C20%2C-3x%5E2%29\"

\n" ); document.write( "Note those first two transformations can be done in either order; or they can be combined into a single transformation \"reflect in the x-axis and stretch vertically by a factor of 3\"

\n" ); document.write( "Last the graph is translated down 5 units: f(x) = -3x^2-5:

\n" ); document.write( "\"graph%28400%2C400%2C-4%2C4%2C-50%2C20%2C-3x%5E2-5%29\"

\n" ); document.write( "It might be helpful to see the graphs of all the stages of the transformation on a single graph:

\n" ); document.write( "\"graph%28400%2C400%2C-4%2C4%2C-50%2C20%2Cx%5E2%2C-x%5E2%2C-3x%5E2%2C-3x%5E2-5%29\"

\n" ); document.write( "red: parent graph, f(x) = x^2
\n" ); document.write( "green: reflected about the x-axis, f(x) = -x^2
\n" ); document.write( "blue: stretched by a vertical factor of 3, f(x) = -3x^2
\n" ); document.write( "purple: translated down 5 units, f(x) = -3x^2-5 \n" ); document.write( "
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