document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=466195>Question 466195</A>: <I><SPAN STYLE=\"word-break: break-all;\"> graph the function f by starting with the graph of y = x2 and using transformations (shifting, compressing, stretching, and/or reflection). \r<BR>\n" );
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document.write( "[Hint: If necessary, write f in the form f(x) = a(x – h)2 + k.]\r<BR>\n" );
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document.write( "f(x) = –2x2 + 6x + 2 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #319526 by </B><A HREF=/tutors/aboutme.mpl?userid=lwsshak3><B>lwsshak3(11628)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=lwsshak3><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=319526\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> graph the function f by starting with the graph of y = x2 and using transformations (shifting, compressing, stretching, and/or reflection). <BR>\n" );
document.write( "[Hint: If necessary, write f in the form f(x) = a(x – h)2 + k.] <BR>\n" );
document.write( "f(x) = –2x2 + 6x + 2<BR>\n" );
document.write( "..<BR>\n" );
document.write( " –2x^2 + 6x + 2<BR>\n" );
document.write( "completing the square<BR>\n" );
document.write( "-2(x^2-3x+9/4)+2+9/2<BR>\n" );
document.write( "-2(x-3/2)^2+13/2<BR>\n" );
document.write( "This is a parabola of the standard form, y=A(x-h)^2+k, with h=3/2 and k=13/2, and it opens downward.<BR>\n" );
document.write( "see the graph of this parabola as follows:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+graph%28+300%2C+300%2C+-10%2C+10%2C+-10%2C+10%2C-2%28x-3%2F2%29%5E2%2B13%2F2%29+ ALIGN=MIDDLE  ALT=\"+graph%28+300%2C+300%2C+-10%2C+10%2C+-10%2C+10%2C-2%28x-3%2F2%29%5E2%2B13%2F2%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "..<BR>\n" );
document.write( "The next graph shows the result of removing the coefficient A=2. Notice how the curve is a little wider or less steep. The larger this coefficient, the steeper the curve.<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+graph%28+300%2C+300%2C+-10%2C+10%2C+-10%2C+10%2C+-%28x-3%2F2%29%5E2%2B13%2F2%29+ ALIGN=MIDDLE  ALT=\"+graph%28+300%2C+300%2C+-10%2C+10%2C+-10%2C+10%2C+-%28x-3%2F2%29%5E2%2B13%2F2%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "..<BR>\n" );
document.write( "The next graph shows the result of removing (h,k) the (x,y) coordinates of the vertex.<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+graph%28+300%2C+300%2C+-10%2C+10%2C+-10%2C+10%2C+-x%5E2%29+ ALIGN=MIDDLE  ALT=\"+graph%28+300%2C+300%2C+-10%2C+10%2C+-10%2C+10%2C+-x%5E2%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "..<BR>\n" );
document.write( "Removing the negative coefficient<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+graph%28+300%2C+300%2C+-10%2C+10%2C+-10%2C+10%2C+x%5E2%29+ ALIGN=MIDDLE  ALT=\"+graph%28+300%2C+300%2C+-10%2C+10%2C+-10%2C+10%2C+x%5E2%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ".. </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );