document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=23329>Question 23329</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Can you help me with this problem and help me sketch a graph<BR>\n" );
document.write( "y = x^2 + 2x -24\r<BR>\n" );
document.write( "\n" );
document.write( "Thanks,<BR>\n" );
document.write( "M </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #12107 by </B><A HREF=/tutors/aboutme.mpl?userid=philberg99><B>philberg99(10)</B></A><img src=\"/images/stars/stars-05.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=philberg99><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=12107\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> First of all, look at the coefficient 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.  If it is positive, then the parabola is shaped up.  If it is negative, the parabola is shaped down.  The coefficient 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 is 1 so it is shaped up.\r<BR>\n" );
document.write( "\n" );
document.write( "Now we have to figure out where the parabola crosses the x axis.  To do this, set the equation equal to zero. \r<BR>\n" );
document.write( "\n" );
document.write( "0 = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2+%2B+2%2Ax+-+24 ALIGN=MIDDLE  ALT=\"x%5E2+%2B+2%2Ax+-+24\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "0 = (x - 4)(x + 6)<BR>\n" );
document.write( "0 = x - 4, 0 = x + 6\r<BR>\n" );
document.write( "\n" );
document.write( "So x = 4, x = -6 are our solutions.\r<BR>\n" );
document.write( "\n" );
document.write( "Finally, you may need to find the lowest point of this parabola, called the vertex.  To find the x coordinate of the vertex, use the formula x = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28-b%29%2F%282%2Aa%29 ALIGN=MIDDLE  ALT=\"%28-b%29%2F%282%2Aa%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > where a is the coefficient 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 and b is the coefficient of the <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x ALIGN=MIDDLE  ALT=\"x\"   DISABLED_style= \"max-width:90%; height:auto;\" > term.  So x = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28-2%29%2F%282%2A1%29%7D%7D%2C+so+x+=+%7B%7B%7B%28-2%29%2F2 ALIGN=MIDDLE  ALT=\"%28-2%29%2F%282%2A1%29%7D%7D%2C+so+x+=+%7B%7B%7B%28-2%29%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" > = -1.  To find the y value that goes with the -1, substitute -1 in for x.  That gives us y = (-1)^2 + 2(-1) - 24 = 1 - 2 - 24 = -25.  So the vertex, or the lowest point of the parabola is (-1, -25). </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );