document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=358803>Question 358803</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Given the following 3 points, find the particular equation.  Graph the parabola.  Label the axis of symmetry, vertex, y-intercept and its symmetric partner, and the x-intercepts.<BR>\n" );
document.write( "(3,138)  (10, 292)    (15, 282) </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #256196 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=256196\">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=y=ax%5E2%2Bbx%2Bc ALIGN=MIDDLE  ALT=\"y=ax%5E2%2Bbx%2Bc\"   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=138=a%283%29%5E2%2Bb%283%29%2Bc ALIGN=MIDDLE  ALT=\"138=a%283%29%5E2%2Bb%283%29%2Bc\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "1.<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=9a%2B3b%2Bc=138 ALIGN=MIDDLE  ALT=\"9a%2B3b%2Bc=138\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ".<BR>\n" );
document.write( ".<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=292=a%2810%29%5E2%2Bb%2810%29%2Bc ALIGN=MIDDLE  ALT=\"292=a%2810%29%5E2%2Bb%2810%29%2Bc\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "2.<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=100a%2B10b%2Bc=292 ALIGN=MIDDLE  ALT=\"100a%2B10b%2Bc=292\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ".<BR>\n" );
document.write( ".<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=282=a%2815%29%5E2%2Bb%2815%29%2Bc ALIGN=MIDDLE  ALT=\"282=a%2815%29%5E2%2Bb%2815%29%2Bc\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "3.<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=225a%2B15b%2Bc=282 ALIGN=MIDDLE  ALT=\"225a%2B15b%2Bc=282\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Subtract eq. 1 from eq. 2 to eliminate <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=c ALIGN=MIDDLE  ALT=\"c\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=100a%2B10b%2Bc-9a-3b-c=292-138 ALIGN=MIDDLE  ALT=\"100a%2B10b%2Bc-9a-3b-c=292-138\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=91a%2B7b=154 ALIGN=MIDDLE  ALT=\"91a%2B7b=154\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "4.<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=13a%2Bb=22 ALIGN=MIDDLE  ALT=\"13a%2Bb=22\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Subtract eq. 1 from eq. 3 to eliminate <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=c ALIGN=MIDDLE  ALT=\"c\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=225a%2B15b%2Bc-9a-3b-c=282-138 ALIGN=MIDDLE  ALT=\"225a%2B15b%2Bc-9a-3b-c=282-138\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=216a%2B12b=144 ALIGN=MIDDLE  ALT=\"216a%2B12b=144\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "5.<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=18a%2Bb=12 ALIGN=MIDDLE  ALT=\"18a%2Bb=12\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Subtract eq. 4 from eq. 5 to eliminate <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=18a%2Bb-13a%2Bb=12-22 ALIGN=MIDDLE  ALT=\"18a%2Bb-13a%2Bb=12-22\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5a=-10 ALIGN=MIDDLE  ALT=\"5a=-10\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28+a=-2%29 ALIGN=MIDDLE  ALT=\"highlight%28+a=-2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Then,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-36%2Bb=12 ALIGN=MIDDLE  ALT=\"-36%2Bb=12\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28+b=48%29 ALIGN=MIDDLE  ALT=\"highlight%28+b=48%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Then,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-18%2B144%2Bc=138 ALIGN=MIDDLE  ALT=\"-18%2B144%2Bc=138\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28+c=12%29 ALIGN=MIDDLE  ALT=\"highlight%28+c=12%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ".<BR>\n" );
document.write( ".<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight_green%28y=-2x%5E2%2B48x%2B12%29 ALIGN=MIDDLE  ALT=\"highlight_green%28y=-2x%5E2%2B48x%2B12%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ".<BR>\n" );
document.write( ".<BR>\n" );
document.write( "Convert to vertex form, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=a%28x-h%29%5E2%2Bk ALIGN=MIDDLE  ALT=\"y=a%28x-h%29%5E2%2Bk\"   DISABLED_style= \"max-width:90%; height:auto;\" >, by completing the square.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=-2%28x%5E2-24x%29%2B12 ALIGN=MIDDLE  ALT=\"y=-2%28x%5E2-24x%29%2B12\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=-2%28x%5E2-24x%2B144%29%2B12%2B2%28144%29 ALIGN=MIDDLE  ALT=\"y=-2%28x%5E2-24x%2B144%29%2B12%2B2%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=y=-2%28x-12%29%5E2%2B12%2B288 ALIGN=MIDDLE  ALT=\"y=-2%28x-12%29%5E2%2B12%2B288\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=-2%28x-12%29%5E2%2B300 ALIGN=MIDDLE  ALT=\"y=-2%28x-12%29%5E2%2B300\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "The vertex is (<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=12 ALIGN=MIDDLE  ALT=\"12\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=300 ALIGN=MIDDLE  ALT=\"300\"   DISABLED_style= \"max-width:90%; height:auto;\" >).<BR>\n" );
document.write( ".<BR>\n" );
document.write( ".<BR>\n" );
document.write( "The vertex lies on the axis of symmetry <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=12 ALIGN=MIDDLE  ALT=\"x=12\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( ".<BR>\n" );
document.write( ".<BR>\n" );
document.write( "The y-intercept is,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=-2%280%29%5E2%2B48%280%29%2B12=12 ALIGN=MIDDLE  ALT=\"y=-2%280%29%5E2%2B48%280%29%2B12=12\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Its symmetric partner would be <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=12%2B12=24 ALIGN=MIDDLE  ALT=\"x=12%2B12=24\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=12 ALIGN=MIDDLE  ALT=\"y=12\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=24 ALIGN=MIDDLE  ALT=\"24\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=12 ALIGN=MIDDLE  ALT=\"12\"   DISABLED_style= \"max-width:90%; height:auto;\" >)<BR>\n" );
document.write( ".<BR>\n" );
document.write( ".<BR>\n" );
document.write( "The x-intercepts are,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-2%28x-12%29%5E2%2B300=0 ALIGN=MIDDLE  ALT=\"-2%28x-12%29%5E2%2B300=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%28x-12%29%5E2=300 ALIGN=MIDDLE  ALT=\"2%28x-12%29%5E2=300\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x-12%29%5E2=150 ALIGN=MIDDLE  ALT=\"%28x-12%29%5E2=150\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x-12=0+%2B-+sqrt%28150%29 ALIGN=MIDDLE  ALT=\"x-12=0+%2B-+sqrt%28150%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=12+%2B-+5%2Asqrt%286%29 ALIGN=MIDDLE  ALT=\"x=12+%2B-+5%2Asqrt%286%29\"   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=drawing%28300%2C300%2C-5%2C25%2C-50%2C350%2Ccircle%2812+%2B5%2Asqrt%286%29%2C0%2C0.6%29%2Ccircle%2812-+5%2Asqrt%286%29%2C0%2C0.6%29%2Ccircle%283%2C138%2C0.6%29%2Ccircle%280%2C12%2C0.6%29%2Ccircle%2810%2C292%2C0.6%29%2Ccircle%2815%2C282%2C0.6%29%2Ccircle%2824%2C12%2C0.6%29%2Ccircle%2812%2C300%2C0.6%29%2Cgrid%281%29%2Cblue%28line%2812%2C-300%2C12%2C500%29%29%2Cgraph%28300%2C300%2C-5%2C25%2C-50%2C350%2C-2x%5E2%2B48x%2B12%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" );