document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=23010>Question 23010</A>: <I><SPAN STYLE=\"word-break: break-all;\"> last question.  I have a problem figuring out how to graph the quadratic function.  I need to understand how to do this can someone explain it to me please.  thank u very much.  the question says begin by graphing the standard quadratic function f(x)=x^2.  The use transformation of this graph to graph the given function.  g(x)=-1/2(x-3)^2-3    i am not understanding it.  Help please<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #11408 by </B><A HREF=/tutors/aboutme.mpl?userid=rapaljer><B>rapaljer(4671)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=rapaljer><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/cgi-bin/show-face.mpl?user=rapaljer><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=11408\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Begin with <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29+=+x%5E2 ALIGN=MIDDLE  ALT=\"f%28x%29+=+x%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28300%2C300%2C+-10%2C+10%2C+-10%2C10%2C+x%5E2+%29+ ALIGN=MIDDLE  ALT=\"graph%28300%2C300%2C+-10%2C+10%2C+-10%2C10%2C+x%5E2+%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Next, what happens if you make that <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+%281%2F2%29%2Ax%5E2 ALIGN=MIDDLE  ALT=\"+%281%2F2%29%2Ax%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >?\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28300%2C300%2C+-10%2C+10%2C+-10%2C10%2C+%281%2F2%29%2Ax%5E2+%29+ ALIGN=MIDDLE  ALT=\"graph%28300%2C300%2C+-10%2C+10%2C+-10%2C10%2C+%281%2F2%29%2Ax%5E2+%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Answer:  It opens the graph up to a broader shape!\r<BR>\n" );
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document.write( "Now, what happens if you make the function negative <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-%281%2F2%29%2Ax%5E2+ ALIGN=MIDDLE  ALT=\"-%281%2F2%29%2Ax%5E2+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28300%2C300%2C+-10%2C+10%2C+-10%2C10%2C+-%281%2F2%29%2Ax%5E2+%29+ ALIGN=MIDDLE  ALT=\"graph%28300%2C300%2C+-10%2C+10%2C+-10%2C10%2C+-%281%2F2%29%2Ax%5E2+%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Answer:  It inverts the graph!\r<BR>\n" );
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document.write( "Now what happens if you make that <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-%281%2F2%29%2A%28x-3%29%5E2 ALIGN=MIDDLE  ALT=\"-%281%2F2%29%2A%28x-3%29%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28300%2C300%2C+-10%2C+10%2C+-10%2C10%2C+-%281%2F2%29%2A%28x-3%29%5E2+%29+ ALIGN=MIDDLE  ALT=\"graph%28300%2C300%2C+-10%2C+10%2C+-10%2C10%2C+-%281%2F2%29%2A%28x-3%29%5E2+%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Answer:  It moves the graph 3 units to the right!\r<BR>\n" );
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document.write( "Finally, what happens if you subtract 3 from the previous function?<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28300%2C300%2C+-10%2C+10%2C+-10%2C10%2C+-%281%2F2%29%2A%28x-3%29%5E2+-3%29+ ALIGN=MIDDLE  ALT=\"graph%28300%2C300%2C+-10%2C+10%2C+-10%2C10%2C+-%281%2F2%29%2A%28x-3%29%5E2+-3%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Answer:  It moves the graph down three units.\r<BR>\n" );
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document.write( "Pretty neat, huh??\r<BR>\n" );
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document.write( "R^2 at SCC<BR>\n" );
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