document.write( "Question 59415: Explain how the graph of y-5=(x-3)^2 can be obtained from the graph of y=x^2. \n" ); document.write( "

Algebra.Com's Answer #40712 by funmath(2933) $\"\"$ $\"About$

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Explain how the graph of y-5=(x-3)^2 can be obtained from the graph of y=x^2.
\n" ); document.write( "The graph of y=x^2 looks like:
\n" ); document.write( " $\"graph%28300%2C200%2C-10%2C10%2C-10%2C10%2Cx%5E2%29\"$
\n" ); document.write( "The graph of y-5=(x-3)^2 looks exacltly the same, but rather than having a vertex at (0,0), it has a vertex at:
\n" ); document.write( "x-3=0 and y-5=0
\n" ); document.write( "x=3 and y=5
\n" ); document.write( "It's vertex is: (3,5)
\n" ); document.write( "A lot of books are teaching that it has a horizontal shift 3 units to the right and a vertical shift five units up.
\n" ); document.write( "y=(x-3)^2+5 The horizontal shift is a result of the -3 (3 units to the right) inside the parenthesis and the vertical shift is a result of the +5 (5 units up) outside of the parenthesis.
\n" ); document.write( "It looks like this:
\n" ); document.write( " $\"graph%28300%2C200%2C-10%2C10%2C-10%2C10%2C%28x-3%29%5E2%2B5%29\"$
\n" ); document.write( "Happy Calculating!!! \n" ); document.write( "

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