document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=240777>Question 240777</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Let f(x)=3x^2-8x. find a such that f(a)=-5. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #176383 by </B><A HREF=/tutors/aboutme.mpl?userid=jsmallt9><B>jsmallt9(3758)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jsmallt9><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=176383\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> If <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29+=+3x%5E2-8x ALIGN=MIDDLE  ALT=\"f%28x%29+=+3x%5E2-8x\"   DISABLED_style= \"max-width:90%; height:auto;\" >, then <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28a%29+=+3a%5E2+-8a ALIGN=MIDDLE  ALT=\"f%28a%29+=+3a%5E2+-8a\"   DISABLED_style= \"max-width:90%; height:auto;\" >. And if f(a) = -5 then <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-5+=+3a%5E2+-8a ALIGN=MIDDLE  ALT=\"-5+=+3a%5E2+-8a\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<br><BR>\n" );
document.write( "Now we just solve for a. Since this is a quadratic equation we will<BR>\n" );
document.write( "1) Get one side equal to zero (by adding 5 to each side):<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0+=+3a%5E2+-+8a+%2B5 ALIGN=MIDDLE  ALT=\"0+=+3a%5E2+-+8a+%2B5\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "2) Factor (and use the Zero Product Property) or use the Quadratic Formula.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0+=+%283a+-+5%29%28a-1%29 ALIGN=MIDDLE  ALT=\"0+=+%283a+-+5%29%28a-1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "By the Zero Product Property, this or any product can be zero only if one (or more) of the factors is zero. So<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3a+-+5+=+0 ALIGN=MIDDLE  ALT=\"3a+-+5+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a-1+=+0 ALIGN=MIDDLE  ALT=\"a-1+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Solving these two equations we get:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3a+=+5 ALIGN=MIDDLE  ALT=\"3a+=+5\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <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>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a+=+5%2F3 ALIGN=MIDDLE  ALT=\"a+=+5%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" > of <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;\" > (You will get these same answers if you use the Quadratic formula correctly.) </SPAN>\n" );
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