document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=113917>Question 113917</A>: <I><SPAN STYLE=\"word-break: break-all;\"> hey,<BR>\n" );
document.write( "could  u please solve this equation.<BR>\n" );
document.write( "find the quadratic relation in vertex form that has zeros -3 and 5 and passes through (3,6).\r<BR>\n" );
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document.write( "i found x-value which is the axis of symmetry -3+5= 2/2 = 1<BR>\n" );
document.write( "Therefore x=1\r<BR>\n" );
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document.write( "but i could not find the y-value\r<BR>\n" );
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document.write( "Please could u sovle it and send me back.<BR>\n" );
document.write( "i will be waithing,\r<BR>\n" );
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document.write( "thank you,<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 #82898 by </B><A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><B>jim_thompson5910(35256)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><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=82898\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Since the zeros are <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=-3 ALIGN=MIDDLE  ALT=\"x=-3\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <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;\" > we can find the factorization using these zeros. We simply need to use the zero product property in reverse\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=-3 ALIGN=MIDDLE  ALT=\"x=-3\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <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;\" > Start with the given solutions\r<BR>\n" );
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document.write( "<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;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x-5=0 ALIGN=MIDDLE  ALT=\"x-5=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > Get the numbers to the left side\r<BR>\n" );
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document.write( "Since either piece equals zero, then their product equals zero\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%2B3%29%28x-5%29=0 ALIGN=MIDDLE  ALT=\"%28x%2B3%29%28x-5%29=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "However, this equation may not pass through (3,6). So let's introduce an \"a\" coefficient in front to get the equation:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=a%28x%2B3%29%28x-5%29 ALIGN=MIDDLE  ALT=\"y=a%28x%2B3%29%28x-5%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Now since the equation passes through (3,6), this means x=3 and y=6\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6=a%283%2B3%29%283-5%29 ALIGN=MIDDLE  ALT=\"6=a%283%2B3%29%283-5%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Plug in x=3 and y=6\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6=a%286%29%28-2%29 ALIGN=MIDDLE  ALT=\"6=a%286%29%28-2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Combine like terms\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6=a%28-12%29 ALIGN=MIDDLE  ALT=\"6=a%28-12%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6%2F%28-12%29=a ALIGN=MIDDLE  ALT=\"6%2F%28-12%29=a\"   DISABLED_style= \"max-width:90%; height:auto;\" > Divide both sides by -12\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-1%2F2=a ALIGN=MIDDLE  ALT=\"-1%2F2=a\"   DISABLED_style= \"max-width:90%; height:auto;\" > Reduce\r<BR>\n" );
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document.write( "So our answer is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a=-1%2F2 ALIGN=MIDDLE  ALT=\"a=-1%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" > which means the equation is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=%28-1%2F2%29%28x%2B3%29%28x-5%29 ALIGN=MIDDLE  ALT=\"y=%28-1%2F2%29%28x%2B3%29%28x-5%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Notice if we graph <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=%28-1%2F2%29%28x%2B3%29%28x-5%29 ALIGN=MIDDLE  ALT=\"y=%28-1%2F2%29%28x%2B3%29%28x-5%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > and plot the point (3,6), we can see that the point lies on the line and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=%28-1%2F2%29%28x%2B3%29%28x-5%29 ALIGN=MIDDLE  ALT=\"y=%28-1%2F2%29%28x%2B3%29%28x-5%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > has zeros -3 and 5. So this verifies our answer. \r<BR>\n" );
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