document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=231995>Question 231995</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Find the x-intercepts of the parabola with vertex (6,-5) and y-intercept (o,175). Write your answer in this form: (x1,y1),(x2,y2). If necessary, round to the nearest hundredth. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #171549 by </B><A HREF=/tutors/aboutme.mpl?userid=josmiceli><B>josmiceli(19441)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=josmiceli><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=josmiceli><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=171549\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> If the equation is in the form<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+ax%5E2+%2B+bx+%2B+c ALIGN=MIDDLE  ALT=\"y+=+ax%5E2+%2B+bx+%2B+c\"   DISABLED_style= \"max-width:90%; height:auto;\" > , then the x component<BR>\n" );
document.write( "of the vertex is at <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-%28b%2F2a%29%29%29%0D%0Agiven%3A%0D%0Avertex+is+at+%286%2C-5%29%2C+so%0D%0A%281%29+%7B%7B%7B6+=+-%28b%2F2a%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "and, plugging the point into general equation,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+ax%5E2+%2B+bx+%2B+c ALIGN=MIDDLE  ALT=\"y+=+ax%5E2+%2B+bx+%2B+c\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-5+=+a%2A6%5E2+%2B+b%2A6+%2B+c ALIGN=MIDDLE  ALT=\"-5+=+a%2A6%5E2+%2B+b%2A6+%2B+c\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(2) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-5+=+36a+%2B+6b+%2B+c ALIGN=MIDDLE  ALT=\"-5+=+36a+%2B+6b+%2B+c\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "---------------------------<BR>\n" );
document.write( "The y-intercept is at (0,175), so plugging this into<BR>\n" );
document.write( "general equation:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=175+=+a%2A0%5E2+%2B+b%2A0+%2B+c ALIGN=MIDDLE  ALT=\"175+=+a%2A0%5E2+%2B+b%2A0+%2B+c\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(3) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=175+=+c ALIGN=MIDDLE  ALT=\"175+=+c\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Now I have 3 equations and 3 unknowns, so it's solvable<BR>\n" );
document.write( "From (1),<BR>\n" );
document.write( "(1) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6+=+-%28b%2F2a%29 ALIGN=MIDDLE  ALT=\"6+=+-%28b%2F2a%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b+=+-12a ALIGN=MIDDLE  ALT=\"b+=+-12a\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Plug this into (2)<BR>\n" );
document.write( "(2) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-5+=+36a+%2B+6b+%2B+c ALIGN=MIDDLE  ALT=\"-5+=+36a+%2B+6b+%2B+c\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(2) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-5+=+36a+%2B+6%2A%28-12a%29+%2B+c ALIGN=MIDDLE  ALT=\"-5+=+36a+%2B+6%2A%28-12a%29+%2B+c\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "also, from(3),<BR>\n" );
document.write( "(2) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-5+=+36a+%2B+6%2A%28-12a%29+%2B+175 ALIGN=MIDDLE  ALT=\"-5+=+36a+%2B+6%2A%28-12a%29+%2B+175\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=36a+-+72a+=+-175+-5 ALIGN=MIDDLE  ALT=\"36a+-+72a+=+-175+-5\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-36a+=+-180 ALIGN=MIDDLE  ALT=\"-36a+=+-180\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a+=+5 ALIGN=MIDDLE  ALT=\"a+=+5\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "and, since<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b+=+-12a ALIGN=MIDDLE  ALT=\"b+=+-12a\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b+=+-12%2A5 ALIGN=MIDDLE  ALT=\"b+=+-12%2A5\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b+=+-60 ALIGN=MIDDLE  ALT=\"b+=+-60\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Now I can write the actual equation<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+5x%5E2+-+60x+%2B+175 ALIGN=MIDDLE  ALT=\"y+=+5x%5E2+-+60x+%2B+175\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Set <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+0 ALIGN=MIDDLE  ALT=\"y+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" > to find x-intercepts<BR>\n" );
document.write( "Then divide through by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5 ALIGN=MIDDLE  ALT=\"5\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2+-+12x+%2B+35+=+0 ALIGN=MIDDLE  ALT=\"x%5E2+-+12x+%2B+35+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "I can see right away that it factors into<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x+-+5%29%28x+-+7%29+=+0 ALIGN=MIDDLE  ALT=\"%28x+-+5%29%28x+-+7%29+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+5 ALIGN=MIDDLE  ALT=\"x+=+5\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+7 ALIGN=MIDDLE  ALT=\"x+=+7\"   DISABLED_style= \"max-width:90%; height:auto;\" > are the solutions<BR>\n" );
document.write( "So, the x-intercepts are at (5,0) and (7,0)\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );