document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=350825>Question 350825</A>: <I><SPAN STYLE=\"word-break: break-all;\"> how do you figure out the height of the max/min when drawin a quadratic parobola???\r<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #250812 by </B><A HREF=/tutors/aboutme.mpl?userid=Theo><B>Theo(13342)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Theo><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=Theo><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=250812\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> x = -b /2a is the formula to get the x value of the maximum / minimum\r<BR>\n" );
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document.write( "once you get that, then you get f(-b/2a) to get the y value.\r<BR>\n" );
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document.write( "the point pair (x,f(x)) becomes (-b/2a, f(-b/2a)) becomes the maximum / minimum point.\r<BR>\n" );
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document.write( "if the coefficient of the x^2 term is positive, then the max/min point is a minimum point.\r<BR>\n" );
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document.write( "if the coefficient of the x^2 term is negative, then the max/min point is a maximum point.\r<BR>\n" );
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document.write( "some examples:\r<BR>\n" );
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document.write( "y = f(x) = x^2 + 2x + 3\r<BR>\n" );
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document.write( "the equation is in standard form of ax^2 + bx + c, so:\r<BR>\n" );
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document.write( "a = 1<BR>\n" );
document.write( "b = 2<BR>\n" );
document.write( "c = 3\r<BR>\n" );
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document.write( "x value of max/min point is x = -b/2a which becomes -2/2 which becomes -1.\r<BR>\n" );
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document.write( "the y value of max/min point is y = f(x) = f(-b/2a) = f(-1).\r<BR>\n" );
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document.write( "since f(x) = x^2 + 2x + 3, then f(-1) = (-1)^2 + 2*(-1) + 3 which becomes 1 - 2 + 3 which becomes 2.\r<BR>\n" );
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document.write( "the max/min point becomes (-1,2) which means that x = -1, and y = 2.\r<BR>\n" );
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document.write( "coefficient of x^2 term is positive, so this is a min point.\r<BR>\n" );
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document.write( "graph of this equation is shown below:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28600%2C600%2C-5%2C5%2C-5%2C5%2Cx%5E2+%2B+2x+%2B+3%29 ALIGN=MIDDLE  ALT=\"graph%28600%2C600%2C-5%2C5%2C-5%2C5%2Cx%5E2+%2B+2x+%2B+3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "you can see that the max/min point is at (-1,2), and that this is a min point because the coefficient of the x^2 term is positive.\r<BR>\n" );
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document.write( "take the same equation and make the coefficient of the x^2 term negative.\r<BR>\n" );
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document.write( "you get:\r<BR>\n" );
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document.write( "y = f(x) = -x^2 + 2x + 3\r<BR>\n" );
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document.write( "x value of max/min point is still x = -b/2a, only in this case:\r<BR>\n" );
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document.write( "a = -1<BR>\n" );
document.write( "b = 2<BR>\n" );
document.write( "c = 3\r<BR>\n" );
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document.write( "x = -b/2a becomes -2/-2 = 1\r<BR>\n" );
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document.write( "y value of max/min point = f(x) = f(-b/2a) = f(1) = -(1)^2 + 2*1 + 3 = -1 + 2 + 3 = 4\r<BR>\n" );
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document.write( "max/min point becomes (x,y) = (1,4) where x value is equal to 1 and y value is equal to 4.\r<BR>\n" );
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document.write( "graph of this equation is shown below:\r<BR>\n" );
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document.write( "you can see that the max/min point is at (x,y) = (1,4) and that the max/min point is a maximum because the coefficient of the x^2 term is negative. </SPAN>\n" );
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