document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=548218>Question 548218</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Write a quadratic function in standard form with zeros 6 and -8?  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #356797 by </B><A HREF=/tutors/aboutme.mpl?userid=mathie123><B>mathie123(224)</B></A><img src=\"/images/stars/stars-09.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=mathie123><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=356797\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> We know if the quadratic function has zeros 6 and -8 then <BR>\n" );
document.write( "x-6 and x-(-8)=x+8 are both factors of the quadratic function  This means that \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=%28x-6%29%28x%2B8%29 ALIGN=MIDDLE  ALT=\"y=%28x-6%29%28x%2B8%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >   \r<BR>\n" );
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document.write( "Now... standard form is also known as vertex form  and is written as <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=a%28x-h%29%5E2%2Bk ALIGN=MIDDLE  ALT=\"y=a%28x-h%29%5E2%2Bk\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "We can expand our quadratic from above and then put it into this form:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=%28x-6%29%28x%2B8%29 ALIGN=MIDDLE  ALT=\"y=%28x-6%29%28x%2B8%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=x%5E2%2B8x-6x-48 ALIGN=MIDDLE  ALT=\"y=x%5E2%2B8x-6x-48\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=x%5E2%2B2x-48 ALIGN=MIDDLE  ALT=\"y=x%5E2%2B2x-48\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Now we must complete the square to get it into standard form.  To do this, we must add half of the b value squared ((half of 2 is 1 and 1 squared is 1 so we add one).  If we add 1, we must subtract it as well (so we are essentially not changing the equation).   <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=x%5E2%2B2x-48 ALIGN=MIDDLE  ALT=\"y=x%5E2%2B2x-48\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=x%5E2%2B2x%2B1-48-1 ALIGN=MIDDLE  ALT=\"y=x%5E2%2B2x%2B1-48-1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Now taking the first three terms, they can be factored as so:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=%28x%2B1%29%5E2-48-1 ALIGN=MIDDLE  ALT=\"y=%28x%2B1%29%5E2-48-1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=%28x%2B1%29%5E2-49 ALIGN=MIDDLE  ALT=\"y=%28x%2B1%29%5E2-49\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "there we have it:) \r<BR>\n" );
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document.write( "Let me know if you are unsure about anything and I will make sure it is clear for you :) <BR>\n" );
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