document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1111541>Question 1111541</A>: <I><SPAN STYLE=\"word-break: break-all;\"> How do i prove values of a=1/2 and b=2, if given f(x)=-ax^2+bx+c and the tangent to the graph of f at the point (-1;7/2) is 3 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #726539 by </B><A HREF=/tutors/aboutme.mpl?userid=KMST><B>KMST(5328)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=KMST><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=KMST><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=726539\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Something is missing. Is there a typo?<BR>\n" );
document.write( "What was meant by \"the tangent to the graph of f at the point (-1;7/2) is 3\" is not obvious to me.<BR>\n" );
document.write( "Is it that <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3 ALIGN=MIDDLE  ALT=\"3\"   DISABLED_style= \"max-width:90%; height:auto;\" > is the slope of the tangent?<BR>\n" );
document.write( "It could not be that <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=3 ALIGN=MIDDLE  ALT=\"y=3\"   DISABLED_style= \"max-width:90%; height:auto;\" > is the equation<BR>\n" );
document.write( "of the straight line tangent to the graph at the point (-1,7/2),<BR>\n" );
document.write( "because that line must contain the point (-1,7/2).<BR>\n" );
document.write( " <BR>\n" );
document.write( "We are told <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29=-ax%5E2%2Bbx%2Bc ALIGN=MIDDLE  ALT=\"f%28x%29=-ax%5E2%2Bbx%2Bc\"   DISABLED_style= \"max-width:90%; height:auto;\" > , and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28-1%29=-a%28-1%29%5E2%2Bb%28-1%29%2Bc=-a-b%2Bc=7%2F2 ALIGN=MIDDLE  ALT=\"f%28-1%29=-a%28-1%29%5E2%2Bb%28-1%29%2Bc=-a-b%2Bc=7%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( "The slope of the tangent to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29=-ax%5E2%2Bbx%2Bc ALIGN=MIDDLE  ALT=\"f%28x%29=-ax%5E2%2Bbx%2Bc\"   DISABLED_style= \"max-width:90%; height:auto;\" > at a point with any <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x ALIGN=MIDDLE  ALT=\"x\"   DISABLED_style= \"max-width:90%; height:auto;\" > is<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=df%2Fdx=-2ax%2Bb ALIGN=MIDDLE  ALT=\"df%2Fdx=-2ax%2Bb\"   DISABLED_style= \"max-width:90%; height:auto;\" > , the derivative of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29 ALIGN=MIDDLE  ALT=\"f%28x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( "When <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=-1 ALIGN=MIDDLE  ALT=\"x=-1\"   DISABLED_style= \"max-width:90%; height:auto;\" > , the value of the derivative is<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-2a%28-1%29%2Bb=2a%2Bb ALIGN=MIDDLE  ALT=\"-2a%28-1%29%2Bb=2a%2Bb\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( " <BR>\n" );
document.write( "If that slope is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3 ALIGN=MIDDLE  ALT=\"3\"   DISABLED_style= \"max-width:90%; height:auto;\" > ,<BR>\n" );
document.write( "we have <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=system%28-a-b%2Bc=7%2F2%2C2a%2Bb=3%29 ALIGN=MIDDLE  ALT=\"system%28-a-b%2Bc=7%2F2%2C2a%2Bb=3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( "That system of equations has infinite solutions,<BR>\n" );
document.write( "so there is no way to prove that a=1/2 and b=2 with<BR>\n" );
document.write( "Knowing just that the tangent at (-1,7/2) has a slope of 3. <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=red%28system%28a=1%2F2%2Cb=2%2Cc=6%29%29 ALIGN=MIDDLE  ALT=\"red%28system%28a=1%2F2%2Cb=2%2Cc=6%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > is one of them, but <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=green%28system%28a=1%2Cb=1%2Cc=11%2F2%29%29 ALIGN=MIDDLE  ALT=\"green%28system%28a=1%2Cb=1%2Cc=11%2F2%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=blue%28system%28a=3%2F2%2Cb=0%2Cc=5%29%29 ALIGN=MIDDLE  ALT=\"blue%28system%28a=3%2F2%2Cb=0%2Cc=5%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "are also among the infinite number of solutions:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=drawing%28300%2C300%2C-3%2C7%2C-1%2C9%2C%0D%0Agraph%28300%2C300%2C-3%2C7%2C-1%2C9%2C-0.5x%5E2%2B2x%2B6%2C-x%5E2%2Bx%2B5.5%2C-1.5x%5E2%2B5%29%2C%0D%0Acircle%28-1%2C3.5%2C0.2%29%2Cline%28-3%2C-2.5%2C1%2C9.5%29%0D%0A%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( " <BR>\n" );
document.write( "Another piece of information would give us another equation,<BR>\n" );
document.write( "which could complete a system of equation with a unique solution. </SPAN>\n" );
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