document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=128196>Question 128196</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Sketch the graph of f(x) = (x-6)^2 + 2. Label all x-intercept, y-intercepts <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 #93859 by </B><A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><B>jim_thompson5910(35256)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><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=93859\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29=%28x-6%29%5E2+%2B+2 ALIGN=MIDDLE  ALT=\"f%28x%29=%28x-6%29%5E2+%2B+2\"   DISABLED_style= \"max-width:90%; height:auto;\" > Start with the given function\r<BR>\n" );
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document.write( "To find the x-intercepts, simply let <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;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0=%28x-6%29%5E2+%2B+2 ALIGN=MIDDLE  ALT=\"0=%28x-6%29%5E2+%2B+2\"   DISABLED_style= \"max-width:90%; height:auto;\" > Plug in <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;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-2=%28x-6%29%5E2 ALIGN=MIDDLE  ALT=\"-2=%28x-6%29%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > Subtract 2 from both sides\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%28-2%29=x-6 ALIGN=MIDDLE  ALT=\"sqrt%28-2%29=x-6\"   DISABLED_style= \"max-width:90%; height:auto;\" > Take the square root of both sides. \r<BR>\n" );
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document.write( "Since you <b>cannot</b> take the square root of a negative number, there are no real x-intercepts. So this means that the graph does <b>not</b> cross the x-axis. So there are no x-intercepts.\r<BR>\n" );
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document.write( "Now to find the y-intercepts, simply plug in <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=0 ALIGN=MIDDLE  ALT=\"x=0\"   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=f%28x%29=%28x-6%29%5E2+%2B+2 ALIGN=MIDDLE  ALT=\"f%28x%29=%28x-6%29%5E2+%2B+2\"   DISABLED_style= \"max-width:90%; height:auto;\" > Start with the given function\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%280%29=%280-6%29%5E2+%2B+2 ALIGN=MIDDLE  ALT=\"f%280%29=%280-6%29%5E2+%2B+2\"   DISABLED_style= \"max-width:90%; height:auto;\" > Plug in <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=0 ALIGN=MIDDLE  ALT=\"x=0\"   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=f%280%29=%28-6%29%5E2+%2B+2 ALIGN=MIDDLE  ALT=\"f%280%29=%28-6%29%5E2+%2B+2\"   DISABLED_style= \"max-width:90%; height:auto;\" > Subtract\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%280%29=36+%2B+2 ALIGN=MIDDLE  ALT=\"f%280%29=36+%2B+2\"   DISABLED_style= \"max-width:90%; height:auto;\" > Square -6 to get 36\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%280%29=38 ALIGN=MIDDLE  ALT=\"f%280%29=38\"   DISABLED_style= \"max-width:90%; height:auto;\" > Add\r<BR>\n" );
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document.write( "So when <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=0 ALIGN=MIDDLE  ALT=\"x=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=38 ALIGN=MIDDLE  ALT=\"y=38\"   DISABLED_style= \"max-width:90%; height:auto;\" >. So the y-intercept is (0,38)\r<BR>\n" );
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document.write( "Now because <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29=%28x-6%29%5E2+%2B+2 ALIGN=MIDDLE  ALT=\"f%28x%29=%28x-6%29%5E2+%2B+2\"   DISABLED_style= \"max-width:90%; height:auto;\" > is in vertex form <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29=a%28x-h%29%5E2+%2B+k ALIGN=MIDDLE  ALT=\"f%28x%29=a%28x-h%29%5E2+%2B+k\"   DISABLED_style= \"max-width:90%; height:auto;\" > where (h,k) is the vertex, we can see that the vertex is (6,2)\r<BR>\n" );
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document.write( "So putting all of this together, we get\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+graph%28+500%2C+500%2C+-10%2C+10%2C+-10%2C+40%2C+%28x-6%29%5E2+%2B+2%29+ ALIGN=MIDDLE  ALT=\"+graph%28+500%2C+500%2C+-10%2C+10%2C+-10%2C+40%2C+%28x-6%29%5E2+%2B+2%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > Graph of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29=%28x-6%29%5E2+%2B+2 ALIGN=MIDDLE  ALT=\"f%28x%29=%28x-6%29%5E2+%2B+2\"   DISABLED_style= \"max-width:90%; height:auto;\" > \r<BR>\n" );
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document.write( "and we can see that there are no x-intercepts, the graph has a y-intercept (0,38), and the vertex is (6,2). So this visually verifies our answer. </SPAN>\n" );
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