document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=92417>Question 92417</A>: <I><SPAN STYLE=\"word-break: break-all;\"> if a graph of f(x)=-3x2+2x+k passes through the point (-1,3), then the value of k is? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #67269 by </B><A HREF=/tutors/aboutme.mpl?userid=bucky><B>bucky(2189)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=bucky><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=67269\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Given:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29=-3%2A%28x%29%5E2+%2B+2x+%2B+k ALIGN=MIDDLE  ALT=\"f%28x%29=-3%2A%28x%29%5E2+%2B+2x+%2B+k\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Substitute y for f(x) to convert the given equation to the equivalent form:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=-3%2A%28x%29%5E2+%2B+2x+%2B+k ALIGN=MIDDLE  ALT=\"y=-3%2A%28x%29%5E2+%2B+2x+%2B+k\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "You are told that the point (-1,3) is on the graph.  That means that when x is -1, the corresponding<BR>\n" );
document.write( "value of y is 3. So you can substitute -1 for x and 3 for y and the equation should still<BR>\n" );
document.write( "be true.  Make these two substitutions and the equation becomes:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3=-3%2A%28-1%29%5E2+%2B+2%28-1%29+%2B+k ALIGN=MIDDLE  ALT=\"3=-3%2A%28-1%29%5E2+%2B+2%28-1%29+%2B+k\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Square the minus one on the right side to get -1*-1 = +1 and the equation becomes:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3=-3%2A%281%29+%2B+2%28-1%29+%2B+k ALIGN=MIDDLE  ALT=\"3=-3%2A%281%29+%2B+2%28-1%29+%2B+k\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Multiply the first two terms on the right side and you get:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3=-3+-2+%2B+k ALIGN=MIDDLE  ALT=\"3=-3+-2+%2B+k\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Combine the first two terms on the right side and the result is:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3+=+-5+%2B+k ALIGN=MIDDLE  ALT=\"3+=+-5+%2B+k\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Get rid of the -5 on the right side by adding +5 to cancel it out.  But if you add +5<BR>\n" );
document.write( "to the right side, you must also add +5 to the left side.  Adding +5 to both sides gives<BR>\n" );
document.write( "you:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=8+=+k ALIGN=MIDDLE  ALT=\"8+=+k\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "and that's your answer.<BR>\n" );
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document.write( "You can check this by replacing k by +8 in the original equation to get:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29+=+-3x%5E2+%2B+2x+%2B+8 ALIGN=MIDDLE  ALT=\"f%28x%29+=+-3x%5E2+%2B+2x+%2B+8\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Then let x = -1 and see if the left side is +3 as the problem said that y should be +3<BR>\n" );
document.write( "when x is -1.<BR>\n" );
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document.write( "Hope this helps you to see your way through this problem.<BR>\n" );
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