document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=514645>Question 514645</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I am in need of some help regarding a problem.  I have tried to work it several times, consulted with several friends, websites, and references sources and cannot figure this problem out.  I am a visual learner, and was wondering if somebody could help me with the process to solve this type of problem.\r<BR>\n" );
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document.write( "Problem #2<BR>\n" );
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document.write( "Find the x-intercepts and y-intercepts<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+f%28x%29+=+-X%5E2+%2B+5X+%2B+24+ ALIGN=MIDDLE  ALT=\"+f%28x%29+=+-X%5E2+%2B+5X+%2B+24+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "x-coordinates of the intercepts are?<BR>\n" );
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document.write( "the y-intercept is?\r<BR>\n" );
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document.write( "Thank you for your assistance.\r<BR>\n" );
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document.write( "Sincerely,\r<BR>\n" );
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document.write( "Christine Fitzerald </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #343515 by </B><A HREF=/tutors/aboutme.mpl?userid=kingme18><B>kingme18(98)</B></A><img src=\"/images/stars/stars-08.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=kingme18><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=kingme18><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=343515\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The y-intercept is the easy one, so let's start there.  The point where a function intersects the y-axis ALWAYS has an x-coordinate of 0 (to plot the point, you haven't moved left or right at all, you've only moved up or down).  Thus, to find the y-intercept, we can just plug in 0 for x.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+f%28x%29+=+-X%5E2+%2B+5X+%2B+24+ ALIGN=MIDDLE  ALT=\"+f%28x%29+=+-X%5E2+%2B+5X+%2B+24+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+f%280%29+=+-%280%29%5E2%2B5%280%29%2B24 ALIGN=MIDDLE  ALT=\"+f%280%29+=+-%280%29%5E2%2B5%280%29%2B24\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+f%280%29+=+24 ALIGN=MIDDLE  ALT=\"+f%280%29+=+24\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "So, the y-intercept is the point (0, 24)\r<BR>\n" );
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document.write( "To find the x-intercept, we do the opposite and plug 0 in for y: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0=-x%5E2%2B5x%2B24 ALIGN=MIDDLE  ALT=\"0=-x%5E2%2B5x%2B24\"   DISABLED_style= \"max-width:90%; height:auto;\" >.  I hate having a negative in front of the <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2 ALIGN=MIDDLE  ALT=\"x%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > term, so let's divide everything by -1 (this will essentially change all the signs; 0 will still be 0 because 0 divided by -1 is still 0).<BR>\n" );
document.write( "Now, we have <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0=x%5E2-5x-24 ALIGN=MIDDLE  ALT=\"0=x%5E2-5x-24\"   DISABLED_style= \"max-width:90%; height:auto;\" >.  This is factorable if we use -8 and 3 (<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-8+%2B+3+=+-5 ALIGN=MIDDLE  ALT=\"-8+%2B+3+=+-5\"   DISABLED_style= \"max-width:90%; height:auto;\" >, the middle term, and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-8+%2A+3+=+-24 ALIGN=MIDDLE  ALT=\"-8+%2A+3+=+-24\"   DISABLED_style= \"max-width:90%; height:auto;\" >, the last term).  So it can be re-written as <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0=%28x-8%29%28x%2B3%29 ALIGN=MIDDLE  ALT=\"0=%28x-8%29%28x%2B3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "Recall that if two things multiply to 0, one of them must be 0 (for example, if <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=8+%2A+x+=+0 ALIGN=MIDDLE  ALT=\"8+%2A+x+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" >, then x=0).  Thus, either <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x-8=0 ALIGN=MIDDLE  ALT=\"x-8=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2B3=0 ALIGN=MIDDLE  ALT=\"x%2B3=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >.  If you solve each for x, you get x=8 or x=-3.  Those are the two solutions when y=0, so those are the two x-intercepts: (8, 0) and (-3, 0). </SPAN>\n" );
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