document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1164935>Question 1164935</A>: <I><SPAN STYLE=\"word-break: break-all;\"> What is the solution for the quadratic equation depicted in the graph? I linked the image.\r<BR>\n" );
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document.write( "https://i.imgur.com/QgAV6kb.gif\r<BR>\n" );
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document.write( "I just can't get these through my head, no matter what I do! \r<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #789360 by </B><A HREF=/tutors/aboutme.mpl?userid=greenestamps><B>greenestamps(13200)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=greenestamps><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=greenestamps><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=789360\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <br><BR>\n" );
document.write( "In factored form, a quadratic equation is of the form<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+a%28x-p%29%28x-q%29 ALIGN=MIDDLE  ALT=\"y+=+a%28x-p%29%28x-q%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "If x is equal to either p or q, then the value of y is zero, because one of the factors (x-p) or (x-q) is zero.<br><BR>\n" );
document.write( "The values p and q -- that make the y value zero -- are called the roots of the equation.<br><BR>\n" );
document.write( "In a graph, that means the graph crosses the x-axis at x=p and at x=q.<br><BR>\n" );
document.write( "In this example, the graph crosses the x-axis at x=-3 and at x=-4.  So the quadratic equation is of the form<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+a%28x-%28-3%29%29%28x-%28-4%29%29 ALIGN=MIDDLE  ALT=\"y+=+a%28x-%28-3%29%29%28x-%28-4%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "or<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+a%28x%2B3%29%28x%2B4%29 ALIGN=MIDDLE  ALT=\"y+=+a%28x%2B3%29%28x%2B4%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "What is left to do is to determine the value of the coefficient a.<br><BR>\n" );
document.write( "To do that, use any point on the graph other than an x-intercept.<br><BR>\n" );
document.write( "In this example, it looks as if y=2 when x=-2.  So plug those coordinates into the formula and solve for a.<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2+=+a%28%28-2%29%2B3%29%28%28-2%29%2B4%29 ALIGN=MIDDLE  ALT=\"2+=+a%28%28-2%29%2B3%29%28%28-2%29%2B4%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2+=+a%281%29%282%29 ALIGN=MIDDLE  ALT=\"2+=+a%281%29%282%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a+=+1 ALIGN=MIDDLE  ALT=\"a+=+1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "So the equation for the graph is<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+1%28x%2B3%29%28x%2B4%29 ALIGN=MIDDLE  ALT=\"y+=+1%28x%2B3%29%28x%2B4%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "or just<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+%28x%2B3%29%28x%2B4%29 ALIGN=MIDDLE  ALT=\"y+=+%28x%2B3%29%28x%2B4%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br>\r<BR>\n" );
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