document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=47648>Question 47648</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Give the equation of the function whose graph is describe.\r<BR>\n" );
document.write( "\n" );
document.write( "The graph of y=x^2 is shifted 4 units to the right. this graph is then vertically stretched by a factor of 5 and reflected across the x-axis.Finally the graph is shifted 8 units upward. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #31473 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=31473\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> start with <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+x%5E2 ALIGN=MIDDLE  ALT=\"y+=+x%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+200%2C+300%2C+-5%2C+5%2C+-4%2C+20%2C+x%5E2%29+ ALIGN=MIDDLE  ALT=\"+graph%28+200%2C+300%2C+-5%2C+5%2C+-4%2C+20%2C+x%5E2%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Shift 4 units to the right<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+%28x-4%29%5E2 ALIGN=MIDDLE  ALT=\"y+=+%28x-4%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+200%2C+300%2C+-2%2C+10%2C+-4%2C+20%2C+%28x-4%29%5E2%29+ ALIGN=MIDDLE  ALT=\"+graph%28+200%2C+300%2C+-2%2C+10%2C+-4%2C+20%2C+%28x-4%29%5E2%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Stretch in the vertical direction by factor of 5<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+5%2A%28x-4%29%5E2 ALIGN=MIDDLE  ALT=\"y+=+5%2A%28x-4%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+200%2C+300%2C+-2%2C+10%2C+-4%2C+20%2C+5%2A%28x-4%29%5E2%29+ ALIGN=MIDDLE  ALT=\"+graph%28+200%2C+300%2C+-2%2C+10%2C+-4%2C+20%2C+5%2A%28x-4%29%5E2%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Reflect about the x-axis<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+-5%2A%28x-4%29%5E2 ALIGN=MIDDLE  ALT=\"y+=+-5%2A%28x-4%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+200%2C+300%2C+-2%2C+10%2C+-20%2C+4%2C+-5%2A%28x-4%29%5E2%29+ ALIGN=MIDDLE  ALT=\"+graph%28+200%2C+300%2C+-2%2C+10%2C+-20%2C+4%2C+-5%2A%28x-4%29%5E2%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Shift 8 units upward<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+-+8+=+-5%2A%28x-4%29%5E2 ALIGN=MIDDLE  ALT=\"y+-+8+=+-5%2A%28x-4%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+200%2C+300%2C+-2%2C+10%2C+-10%2C+20%2C+8-5%2A%28x-4%29%5E2%29+ ALIGN=MIDDLE  ALT=\"+graph%28+200%2C+300%2C+-2%2C+10%2C+-10%2C+20%2C+8-5%2A%28x-4%29%5E2%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Solving for y,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+-+8+=+-5%2A%28x%5E2+-8x+%2B+16%29 ALIGN=MIDDLE  ALT=\"y+-+8+=+-5%2A%28x%5E2+-8x+%2B+16%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+-5%2A%28x%5E2+-8x+%2B16%29+%2B+8 ALIGN=MIDDLE  ALT=\"y+=+-5%2A%28x%5E2+-8x+%2B16%29+%2B+8\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+-5%2Ax%5E2+%2B+40x+-+80+%2B+8 ALIGN=MIDDLE  ALT=\"y+=+-5%2Ax%5E2+%2B+40x+-+80+%2B+8\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+-5%2Ax%5E2+%2B+40x+-72 ALIGN=MIDDLE  ALT=\"y+=+-5%2Ax%5E2+%2B+40x+-72\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Check some values to see if they make sense<BR>\n" );
document.write( "When x = 4,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+-80+%2B+160+-72 ALIGN=MIDDLE  ALT=\"y+=+-80+%2B+160+-72\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+%2B+8 ALIGN=MIDDLE  ALT=\"y+=+%2B+8\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "OK<BR>\n" );
document.write( "Find roots (solve for y=0) use  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+ ALIGN=MIDDLE  ALT=\"x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "where <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%2Ax%5E2+%2B+b%2Ax+%2B+c+=+0 ALIGN=MIDDLE  ALT=\"a%2Ax%5E2+%2B+b%2Ax+%2B+c+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "a = -5<BR>\n" );
document.write( "b = 40<BR>\n" );
document.write( "c = -72<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%28-40+%2B-+sqrt%28+40%5E2-4%2A%28-5%29%2A%28-72%29+%29%29%2F%282%2A%28-5%29%29+ ALIGN=MIDDLE  ALT=\"x+=+%28-40+%2B-+sqrt%28+40%5E2-4%2A%28-5%29%2A%28-72%29+%29%29%2F%282%2A%28-5%29%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%28-40+%2B-+sqrt%281600+-+1440%29%29+%2F+-10 ALIGN=MIDDLE  ALT=\"x+=+%28-40+%2B-+sqrt%281600+-+1440%29%29+%2F+-10\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+4+%2B-+sqrt%28160%29+%2F+-10 ALIGN=MIDDLE  ALT=\"x+=+4+%2B-+sqrt%28160%29+%2F+-10\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+4+%2B-+4%2Asqrt%2810%29+%2F+10 ALIGN=MIDDLE  ALT=\"x+=+4+%2B-+4%2Asqrt%2810%29+%2F+10\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+4+%2B+1.265 ALIGN=MIDDLE  ALT=\"x+=+4+%2B+1.265\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+4+-+1.265 ALIGN=MIDDLE  ALT=\"x+=+4+-+1.265\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "These values make sense according to graph </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );