document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1048919>Question 1048919</A>: <I><SPAN STYLE=\"word-break: break-all;\"> For the parabola whose equation is&#8203; given, determine whether it opens upward or&#8203; downward, find the&#8203; vertex, and find the&#8203; x- and&#8203; y-intercepts.  Then graph the parabola.<BR>\n" );
document.write( "&#8203;f(x)=x squared minus 2 x minus 48 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #664474 by </B><A HREF=/tutors/aboutme.mpl?userid=MathLover1><B>MathLover1(20849)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=MathLover1><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=MathLover1><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=664474\">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=x%5E2+-x+-+48 ALIGN=MIDDLE  ALT=\"f%28x%29=x%5E2+-x+-+48\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "first write it in vertex form <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29=a%28x-h%29%5E2+%2Bk ALIGN=MIDDLE  ALT=\"f%28x%29=a%28x-h%29%5E2+%2Bk\"   DISABLED_style= \"max-width:90%; height:auto;\" > where <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h ALIGN=MIDDLE  ALT=\"h\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=k ALIGN=MIDDLE  ALT=\"k\"   DISABLED_style= \"max-width:90%; height:auto;\" > are <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x ALIGN=MIDDLE  ALT=\"x\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y ALIGN=MIDDLE  ALT=\"y\"   DISABLED_style= \"max-width:90%; height:auto;\" > coordinates of the vertex\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%5E2+-x%29+-+48 ALIGN=MIDDLE  ALT=\"f%28x%29=%28x%5E2+-x%29+-+48\"   DISABLED_style= \"max-width:90%; height:auto;\" >...complete square\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%5E2+-x%2Bb%5E2%29-b%5E2+-+48 ALIGN=MIDDLE  ALT=\"f%28x%29=%28x%5E2+-x%2Bb%5E2%29-b%5E2+-+48\"   DISABLED_style= \"max-width:90%; height:auto;\" >.....since coefficient <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a=1 ALIGN=MIDDLE  ALT=\"a=1\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2ab=-1 ALIGN=MIDDLE  ALT=\"2ab=-1\"   DISABLED_style= \"max-width:90%; height:auto;\" >, find <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b ALIGN=MIDDLE  ALT=\"b\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%2A1b=-1 ALIGN=MIDDLE  ALT=\"2%2A1b=-1\"   DISABLED_style= \"max-width:90%; height:auto;\" >-><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2b=-1 ALIGN=MIDDLE  ALT=\"2b=-1\"   DISABLED_style= \"max-width:90%; height:auto;\" >-><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b=-1%2F2 ALIGN=MIDDLE  ALT=\"b=-1%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "so, we have<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29=%28x%5E2+-x-%28-1%2F2%29%5E2%29-%28-1%2F2%29%5E2+-+48 ALIGN=MIDDLE  ALT=\"f%28x%29=%28x%5E2+-x-%28-1%2F2%29%5E2%29-%28-1%2F2%29%5E2+-+48\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29=%28x-1%2F2%29%5E2-%281%2F4%29+-+48 ALIGN=MIDDLE  ALT=\"f%28x%29=%28x-1%2F2%29%5E2-%281%2F4%29+-+48\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29=%28x-1%2F2%29%5E2-1%2F4+-+192%2F4 ALIGN=MIDDLE  ALT=\"f%28x%29=%28x-1%2F2%29%5E2-1%2F4+-+192%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29=%28x-1%2F2%29%5E2+-+193%2F4 ALIGN=MIDDLE  ALT=\"f%28x%29=%28x-1%2F2%29%5E2+-+193%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "so, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h=1%2F2 ALIGN=MIDDLE  ALT=\"h=1%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=k=-193%2F4 ALIGN=MIDDLE  ALT=\"k=-193%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h=0.5 ALIGN=MIDDLE  ALT=\"h=0.5\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=k=-48.25 ALIGN=MIDDLE  ALT=\"k=-48.25\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "set <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;\" > to find <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x ALIGN=MIDDLE  ALT=\"x\"   DISABLED_style= \"max-width:90%; height:auto;\" >-intercepts\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0=%28x-1%2F2%29%5E2+-+193%2F4 ALIGN=MIDDLE  ALT=\"0=%28x-1%2F2%29%5E2+-+193%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=193%2F4=%28x-1%2F2%29%5E2+ ALIGN=MIDDLE  ALT=\"193%2F4=%28x-1%2F2%29%5E2+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%28193%2F4%29=x-1%2F2+ ALIGN=MIDDLE  ALT=\"sqrt%28193%2F4%29=x-1%2F2+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F2%2Bsqrt%28193%29%2F2=x+ ALIGN=MIDDLE  ALT=\"1%2F2%2Bsqrt%28193%29%2F2=x+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x ALIGN=MIDDLE  ALT=\"x\"   DISABLED_style= \"max-width:90%; height:auto;\" >-intercepts are: \r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=1%2F2%2Bsqrt%28193%29%2F2 ALIGN=MIDDLE  ALT=\"x=1%2F2%2Bsqrt%28193%29%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=1%2F2-sqrt%28193%29%2F2+ ALIGN=MIDDLE  ALT=\"x=1%2F2-sqrt%28193%29%2F2+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=7.5 ALIGN=MIDDLE  ALT=\"x=7.5\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=-6.5%29 ALIGN=MIDDLE  ALT=\"x=-6.5%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "set <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;\" > to find <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y ALIGN=MIDDLE  ALT=\"y\"   DISABLED_style= \"max-width:90%; height:auto;\" >-intercepts\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29=%280-1%2F2%29%5E2+-+193%2F4 ALIGN=MIDDLE  ALT=\"f%28x%29=%280-1%2F2%29%5E2+-+193%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29=%28-1%2F2%29%5E2+-+193%2F4 ALIGN=MIDDLE  ALT=\"f%28x%29=%28-1%2F2%29%5E2+-+193%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29=1%2F4+-+193%2F4 ALIGN=MIDDLE  ALT=\"f%28x%29=1%2F4+-+193%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29=+-+192%2F4 ALIGN=MIDDLE  ALT=\"f%28x%29=+-+192%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29=+-+48 ALIGN=MIDDLE  ALT=\"f%28x%29=+-+48\"   DISABLED_style= \"max-width:90%; height:auto;\" > which is same if you use <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29=x%5E2+-x+-+48 ALIGN=MIDDLE  ALT=\"f%28x%29=x%5E2+-x+-+48\"   DISABLED_style= \"max-width:90%; height:auto;\" >-><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29=0%5E2+-0+-+48=-48 ALIGN=MIDDLE  ALT=\"f%28x%29=0%5E2+-0+-+48=-48\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=7.5 ALIGN=MIDDLE  ALT=\"x=7.5\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=-6.5%29 ALIGN=MIDDLE  ALT=\"x=-6.5%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=drawing%28+600%2C+600%2C+-25%2C+25%2C+-55%2C+50%2C%0D%0Acircle%281%2F2%2C-193%2F4%2C.42%29%2C+locate%281%2F2%2C-193%2F4%2CV%281%2F2%2C-193%2F4%29%29%2C%0D%0A+circle%287.5%2C0%2C.42%29%2Ccircle%28-6.5%2C0%2C.42%29%2C%0D%0A+graph%28+600%2C+600%2C+-25%2C+25%2C+-55%2C+50%2C+x%5E2+-x+-+48%29%29+ ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );