document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=321729>Question 321729</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Given a parabola with intersection points (-1,0), (2,0) and (0,-16) and a line which passes through (-5,-10) and (4,30), find an equation for the line and the parabola and the points of intersection between the two graphs if any. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #230360 by </B><A HREF=/tutors/aboutme.mpl?userid=Fombitz><B>Fombitz(32388)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Fombitz><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=Fombitz><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=230360\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The general equation for a parabola is, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=ax%5E2%2Bbx%2Bc ALIGN=MIDDLE  ALT=\"y=ax%5E2%2Bbx%2Bc\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Plugging in the points you get a system of equations,<BR>\n" );
document.write( "1.<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a-b%2Bc=0 ALIGN=MIDDLE  ALT=\"a-b%2Bc=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "2.<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4a%2B2b%2Bc=0 ALIGN=MIDDLE  ALT=\"4a%2B2b%2Bc=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "3.<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=c=-16 ALIGN=MIDDLE  ALT=\"c=-16\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Substitute eq. 3 into eq. 1 and eq. 2,<BR>\n" );
document.write( "4.<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a-b=16 ALIGN=MIDDLE  ALT=\"a-b=16\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "5.<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4a%2B2b=16 ALIGN=MIDDLE  ALT=\"4a%2B2b=16\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Multiply eq. 4 by 2 and add to eq. 5 to solve for a.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2a-2b%2B4a%2B2b=32%2B16 ALIGN=MIDDLE  ALT=\"2a-2b%2B4a%2B2b=32%2B16\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6a=48 ALIGN=MIDDLE  ALT=\"6a=48\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a=8 ALIGN=MIDDLE  ALT=\"a=8\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Then from eq. 4,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=8-b=16 ALIGN=MIDDLE  ALT=\"8-b=16\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b=-8 ALIGN=MIDDLE  ALT=\"b=-8\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "The parabola is then,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=8x%5E2-8x-16 ALIGN=MIDDLE  ALT=\"y=8x%5E2-8x-16\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ".<BR>\n" );
document.write( ".<BR>\n" );
document.write( ".<BR>\n" );
document.write( "For the line, calculate the slope,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=m=%28y2-y1%29%2F%28x2-x1%29=%2830-%28-10%29%29%2F%284-%28-5%29%29 ALIGN=MIDDLE  ALT=\"m=%28y2-y1%29%2F%28x2-x1%29=%2830-%28-10%29%29%2F%284-%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=m=40%2F9 ALIGN=MIDDLE  ALT=\"m=40%2F9\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Using the point slope form of a line, <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;\" >, use either point to solve for b.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=%2840%2F9%29x%2Bb ALIGN=MIDDLE  ALT=\"y=%2840%2F9%29x%2Bb\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=30=%2840%2F9%29%284%29%2Bb ALIGN=MIDDLE  ALT=\"30=%2840%2F9%29%284%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=b=270%2F9-160%2F9 ALIGN=MIDDLE  ALT=\"b=270%2F9-160%2F9\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b=110%2F9 ALIGN=MIDDLE  ALT=\"b=110%2F9\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "The line is then,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=+%2840%2F9%29x%2B110%2F9 ALIGN=MIDDLE  ALT=\"y=+%2840%2F9%29x%2B110%2F9\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "To find the intersection points set the two function equal to each other and solve for x.<BR>\n" );
document.write( ".<BR>\n" );
document.write( ".<BR>\n" );
document.write( ".<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=drawing%28300%2C300%2C-20%2C20%2C-20%2C40%2Cgrid%281%29%2Ccircle%28-5%2C-10%2C.5%29%2Ccircle%284%2C30%2C0.5%29%2Ccircle%28-1%2C0%2C.5%29%2Ccircle%282%2C0%2C.5%29%2Ccircle%280%2C-16%2C0.5%29%2Cgraph%28300%2C300%2C-20%2C20%2C-20%2C40%2C+%2840%2F9%29x%2B110%2F9%2C+8x%5E2-8x-16%29%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ".<BR>\n" );
document.write( ".<BR>\n" );
document.write( ".<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=8x%5E2-8x-16=%2840%2F9%29x%2B110%2F9 ALIGN=MIDDLE  ALT=\"8x%5E2-8x-16=%2840%2F9%29x%2B110%2F9\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=72x%5E2-72x-144=40x%2B110 ALIGN=MIDDLE  ALT=\"72x%5E2-72x-144=40x%2B110\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=72x%5E2-112x-254=0 ALIGN=MIDDLE  ALT=\"72x%5E2-112x-254=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Use the quadratic formula,<BR>\n" );
document.write( "<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( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%28112+%2B-+sqrt%28112%5E2-4%2A72%2A%28-254%29+%29%29%2F%282%2A72%29+ ALIGN=MIDDLE  ALT=\"x+=+%28112+%2B-+sqrt%28112%5E2-4%2A72%2A%28-254%29+%29%29%2F%282%2A72%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+=+%28112+%2B-+sqrt%2812544%2B73152+%29%29%2F%28144%29+ ALIGN=MIDDLE  ALT=\"x+=+%28112+%2B-+sqrt%2812544%2B73152+%29%29%2F%28144%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+=+%28112+%2B-+sqrt%2885696+%29%29%2F%28144%29+ ALIGN=MIDDLE  ALT=\"x+=+%28112+%2B-+sqrt%2885696+%29%29%2F%28144%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+=+%28112+%2B-+8sqrt%281339+%29%29%2F%28144%29+ ALIGN=MIDDLE  ALT=\"x+=+%28112+%2B-+8sqrt%281339+%29%29%2F%28144%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+=+%2814+%2B-+sqrt%281339+%29%29%2F%2818%29+ ALIGN=MIDDLE  ALT=\"x+=+%2814+%2B-+sqrt%281339+%29%29%2F%2818%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Now that you have the x values, use either equation to solve for y.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );