document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=178329>Question 178329</A>: <I><SPAN STYLE=\"word-break: break-all;\"> 1. Find the equation of a straight line that passes through a point (–1,3) such that it is perpendicular to straight line y - 2x = 5.	\r<BR>\n" );
document.write( "\n" );
document.write( "2. Sketch a graph for a quadratic function given as below:\r<BR>\n" );
document.write( "\n" );
document.write( "	f (x) = x² - x - 6<BR>\n" );
document.write( " <BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #133298 by </B><A HREF=/tutors/aboutme.mpl?userid=jojo14344><B>jojo14344(1513)</B></A><img src=\"/images/stars/stars-12.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jojo14344><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=133298\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> </pre><font size=4><b><BR>\n" );
document.write( "1)We have to remember when 2 lines are perpendicular, the <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=slope=m%5B2%5D ALIGN=MIDDLE  ALT=\"slope=m%5B2%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" > of the other one is \"negative reciprocal\" of the 1st :------><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=m2=-1%2Fm%5B1%5D ALIGN=MIDDLE  ALT=\"m2=-1%2Fm%5B1%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Arranging Line <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y-2x%2B5 ALIGN=MIDDLE  ALT=\"y-2x%2B5\"   DISABLED_style= \"max-width:90%; height:auto;\" > via Slope-intercept form, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=mx%2Bb ALIGN=MIDDLE  ALT=\"y=mx%2Bb\"   DISABLED_style= \"max-width:90%; height:auto;\" >:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=2x%2B5 ALIGN=MIDDLE  ALT=\"y=2x%2B5\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "We can see it has a <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=Slope=m%5B1%5D=2 ALIGN=MIDDLE  ALT=\"Slope=m%5B1%5D=2\"   DISABLED_style= \"max-width:90%; height:auto;\" >, then the line that passes thru point (-1,3) has a slope:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=m%5B2%5D=-1%2F2 ALIGN=MIDDLE  ALT=\"m%5B2%5D=-1%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Via Slope-intercept Form: point (-1,3)<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3=%28-1%2F2%29%28-1%29%2Bb ALIGN=MIDDLE  ALT=\"3=%28-1%2F2%29%28-1%29%2Bb\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3=%281%2F2%29%2Bb ALIGN=MIDDLE  ALT=\"3=%281%2F2%29%2Bb\"   DISABLED_style= \"max-width:90%; height:auto;\" >----><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b=3-%281%2F2%29=%286-1%29%2F2=5%2F2 ALIGN=MIDDLE  ALT=\"b=3-%281%2F2%29=%286-1%29%2F2=5%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" >, Y-Intercept<BR>\n" );
document.write( "Therefore, line eqn. <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=%28-1%2F2%29x%2B%285%2F2%29 ALIGN=MIDDLE  ALT=\"y=%28-1%2F2%29x%2B%285%2F2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > ----> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%2B%281%2F2%29x=5%2F2 ALIGN=MIDDLE  ALT=\"y%2B%281%2F2%29x=5%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" > (Standard form) passes thru point (-1,3) and perpendicular to line <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y-2x=5 ALIGN=MIDDLE  ALT=\"y-2x=5\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "we'll see:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=drawing%28400%2C400%2C-5%2C5%2C-5%2C8%2Cgrid%281%29%2Cgraph%28400%2C400%2C-5%2C5%2C-5%2C8%2C2x%2B5%2C+%28-1%2F2%29x%2B%285%2F2%29%29%2Cblue%28circle%28-1%2C3%2C.15%29%29%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >-----> RED Line>>>> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=2x%2B5 ALIGN=MIDDLE  ALT=\"y=2x%2B5\"   DISABLED_style= \"max-width:90%; height:auto;\" >; GREEN Line>>>> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%2B%281%2F2%29x=5%2F2 ALIGN=MIDDLE  ALT=\"y%2B%281%2F2%29x=5%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ".<BR>\n" );
document.write( "2)Sketch a graph for a quadratic function given as below:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f+%28x%29+=+x%B2+-+x+-+6 ALIGN=MIDDLE  ALT=\"f+%28x%29+=+x%B2+-+x+-+6\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Solving the quadratic:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2-x-6=0 ALIGN=MIDDLE  ALT=\"x%5E2-x-6=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "where<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=system%28a=1%2Cb=-1%2Cc-6%29 ALIGN=MIDDLE  ALT=\"system%28a=1%2Cb=-1%2Cc-6%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-b%2B-sqrt%28b%5E2-4ac%29%29%2F2a=%28-%28-1%29%2B-sqrt%28-1%5E2-4%2A1%2A-6%29%29%2F%282%2A1%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=%281%2B-sqrt%281%2B24%29%29%2F2=%281%2B-sqrt%2825%29%29%2F2 ALIGN=MIDDLE  ALT=\"x=%281%2B-sqrt%281%2B24%29%29%2F2=%281%2B-sqrt%2825%29%29%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=%281%2Bsqrt%2825%29%29%2F2=%281%2B5%29%2F2=6%2F2=highlight%283%29 ALIGN=MIDDLE  ALT=\"x=%281%2Bsqrt%2825%29%29%2F2=%281%2B5%29%2F2=6%2F2=highlight%283%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=%281-sqrt%2825%29%29%2F2=%281-5%29%2F2=-4%2F2=highlight%28-2%29 ALIGN=MIDDLE  ALT=\"x=%281-sqrt%2825%29%29%2F2=%281-5%29%2F2=-4%2F2=highlight%28-2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "X-intercepts--------> (3,0) & (-2,0)<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=drawing%28400%2C400%2C-5%2C5%2C-8%2C5%2Cgrid%281%29%2Cgraph%28400%2C400%2C-5%2C5%2C-8%2C5%2Cx%5E2-x-6%29%2C+blue%28circle%283%2C0%2C.12%29%29%2Cblue%28circle%28-2%2C0%2C.12%29%29%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "Thank you,<BR>\n" );
document.write( "Jojo</pre>\r<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );