document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1037991>Question 1037991</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The question I have is \"Describe how the graph of f(x)=-1/4(x-5)^2 is related to the graph of f(x)=x^2.\"\r<BR>\n" );
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document.write( "I don't need the answer, I have that! \r<BR>\n" );
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document.write( "I have a math final tomorrow and this just a study guide question.<BR>\n" );
document.write( " I need to know HOW my teacher got \"curves down,wider,shifts 5 units right.\" Thank you!  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #652667 by </B><A HREF=/tutors/aboutme.mpl?userid=josmiceli><B>josmiceli(19441)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=josmiceli><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=josmiceli><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=652667\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Heres the plot of just <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+f%28x%29+=+%28+x-5+%29%5E2+ ALIGN=MIDDLE  ALT=\"+f%28x%29+=+%28+x-5+%29%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%28+400%2C+400%2C+-10%2C+10%2C+-10%2C+10%2C+%28+x-5+%29%5E2+%29+ ALIGN=MIDDLE  ALT=\"+graph%28+400%2C+400%2C+-10%2C+10%2C+-10%2C+10%2C+%28+x-5+%29%5E2+%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Here's the plot of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+-%28+x-5+%29%5E2+ ALIGN=MIDDLE  ALT=\"+-%28+x-5+%29%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%28+400%2C+400%2C+-10%2C+10%2C+-10%2C+10%2C+-%28+x-5+%29%5E2+%29+ ALIGN=MIDDLE  ALT=\"+graph%28+400%2C+400%2C+-10%2C+10%2C+-10%2C+10%2C+-%28+x-5+%29%5E2+%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Now you are going to multiply the right side <BR>\n" );
document.write( "( which is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+f%28x%29+ ALIGN=MIDDLE  ALT=\"+f%28x%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > ), by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+1%2F4+ ALIGN=MIDDLE  ALT=\"+1%2F4+\"   DISABLED_style= \"max-width:90%; height:auto;\" >. Every <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+f%28x%29+ ALIGN=MIDDLE  ALT=\"+f%28x%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "that you had before will be smaller because <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+1%2F4+ ALIGN=MIDDLE  ALT=\"+1%2F4+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "is less than <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+1+ ALIGN=MIDDLE  ALT=\"+1+\"   DISABLED_style= \"max-width:90%; height:auto;\" >. The <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+f%28x%29+=+0+ ALIGN=MIDDLE  ALT=\"+f%28x%29+=+0+\"   DISABLED_style= \"max-width:90%; height:auto;\" > point is anchored<BR>\n" );
document.write( "in place, so the whole parabola is not shifted down, it<BR>\n" );
document.write( "has to get wider. Here's the plot of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+f%28x%29+=+-%281%2F4%29%2A%28+x-5+%29%5E2+ ALIGN=MIDDLE  ALT=\"+f%28x%29+=+-%281%2F4%29%2A%28+x-5+%29%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%28+400%2C+400%2C+-15%2C+15%2C+-15%2C+15%2C+-%281%2F4%29%2A%28+x-5+%29%5E2+%29+ ALIGN=MIDDLE  ALT=\"+graph%28+400%2C+400%2C+-15%2C+15%2C+-15%2C+15%2C+-%281%2F4%29%2A%28+x-5+%29%5E2+%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > <BR>\n" );
document.write( "Here's what happens by multiplying by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+4+ ALIGN=MIDDLE  ALT=\"+4+\"   DISABLED_style= \"max-width:90%; height:auto;\" > isnstead<BR>\n" );
document.write( "of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+1%2F4+ ALIGN=MIDDLE  ALT=\"+1%2F4+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+graph%28+400%2C+400%2C+-10%2C+10%2C+-10%2C+10%2C+-4%2A%28+x-5+%29%5E2+%29+ ALIGN=MIDDLE  ALT=\"+graph%28+400%2C+400%2C+-10%2C+10%2C+-10%2C+10%2C+-4%2A%28+x-5+%29%5E2+%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Hope this helps. You have to either memorize what effect<BR>\n" );
document.write( "things have, or figure it out. Figuring out works much better. </SPAN>\n" );
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