document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=203258>Question 203258</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Y = ax^2 + 4x + c\r<BR>\n" );
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document.write( "the maximum is at (1,8)<BR>\n" );
document.write( "the left hand side starts at (-1,0) <BR>\n" );
document.write( "it goes through (0,6) and reaches the maximum then goes down an end at (3,0)\r<BR>\n" );
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document.write( "i need to know the value of c and a. <BR>\n" );
document.write( "I have been stuck on this question for a long time. thank you again\r<BR>\n" );
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document.write( "i dont even know how to get started. <BR>\n" );
document.write( "thank you for taking your time to solve this.  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #153350 by </B><A HREF=/tutors/aboutme.mpl?userid=Earlsdon><B>Earlsdon(6294)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Earlsdon><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=153350\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Given:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=ax%5E2%2B4x%2Bc ALIGN=MIDDLE  ALT=\"ax%5E2%2B4x%2Bc\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Find a and c.<BR>\n" );
document.write( "First, you are told that the maximum (vertex) of the parabola is at (1, 8).<BR>\n" );
document.write( "The value of the x-coordinate of the vertex is given by:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%28-b%29%2F2a ALIGN=MIDDLE  ALT=\"x+=+%28-b%29%2F2a\"   DISABLED_style= \"max-width:90%; height:auto;\" > Substitute b = 4 and x = 1 (from (1, 8)) to get:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1+=+-4%2F2a ALIGN=MIDDLE  ALT=\"1+=+-4%2F2a\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply both sides by a.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a+=+-4%2F2 ALIGN=MIDDLE  ALT=\"a+=+-4%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" > Simplify.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28a+=+-2%29 ALIGN=MIDDLE  ALT=\"highlight%28a+=+-2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > so we have...<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+-2x%5E2%2B4x%2Bc ALIGN=MIDDLE  ALT=\"y+=+-2x%5E2%2B4x%2Bc\"   DISABLED_style= \"max-width:90%; height:auto;\" > Now to find the value of c, just substitute the x- and y-coordinates of any of the points given in the problem. (1, 8) or (-1, 0) or (0, 6) or (3, 0).<BR>\n" );
document.write( "The reason you can do this is because every one of these points lies on the curve (parabola) and thus satisfies the given equation.<BR>\n" );
document.write( "Let's choose the point (0, 6).<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6+=+-2%280%29%5E2%2B4%280%29%2Bc ALIGN=MIDDLE  ALT=\"6+=+-2%280%29%5E2%2B4%280%29%2Bc\"   DISABLED_style= \"max-width:90%; height:auto;\" > Simplify.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight_green%286+=+c%29 ALIGN=MIDDLE  ALT=\"highlight_green%286+=+c%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "The equation is:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28y+=+-2x%5E2%2B4x%2B6%29 ALIGN=MIDDLE  ALT=\"highlight%28y+=+-2x%5E2%2B4x%2B6%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Let's see what the curve looks like!<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28400%2C400%2C-5%2C5%2C-5%2C10%2C-2x%5E2%2B4x%2B6%29 ALIGN=MIDDLE  ALT=\"graph%28400%2C400%2C-5%2C5%2C-5%2C10%2C-2x%5E2%2B4x%2B6%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );