document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=151599>Question 151599</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Ok so I have been stuck on how to figure out vertex of a parabola and the maximum/minimum. I know that if it is a negative number then we should look at maximum. I have a TI-83 calculator but I can't even begin to figure out, if I could do this on the calculator. Here is one example from my book:\r<BR>\n" );
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document.write( "-.2x^2+1.4x-5.9\r<BR>\n" );
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document.write( "Any help would be so appreciated. I need to know how to break down this problem in \"dumb terms\". I look at the book and I get even more confused. Thank you, Thank you, Thank you </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #111431 by </B><A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><B>jim_thompson5910(35256)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><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=111431\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> In order to find the vertex with a calculator, first graph <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=-0.2x%5E2%2B1.4x-5.9 ALIGN=MIDDLE  ALT=\"y=-0.2x%5E2%2B1.4x-5.9\"   DISABLED_style= \"max-width:90%; height:auto;\" >. Now press 2nd and then \"trace\". This will lead you to the \"calc\" menu. Now scroll down to \"maximum\" and hit enter. Find the highest point on the graph and scroll slightly to the left and hit enter. Now scroll past the highest point and go slightly to the right and hit enter. Finally hit enter a third time to let the calculator find the max. Let me know if you have a problem with any of these steps.\r<BR>\n" );
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document.write( "<a  rel=nofollow HREF=\"http://www.itc.csmd.edu/mth/ti83/graph/minmax.htm\">Here's</a> a good tutorial to find the maximum.\r<BR>\n" );
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document.write( "Here's how to find the vertex algebraically (ie without a graphing calculator)\r<BR>\n" );
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document.write( "In order to find the vertex, we first need to find the x-coordinate of the vertex.\r<BR>\n" );
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document.write( "To find the x-coordinate of the vertex, use this formula: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=%28-b%29%2F%282a%29 ALIGN=MIDDLE  ALT=\"x=%28-b%29%2F%282a%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=%28-b%29%2F%282a%29 ALIGN=MIDDLE  ALT=\"x=%28-b%29%2F%282a%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Start with the given formula.\r<BR>\n" );
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document.write( "From <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=-0.2x%5E2%2B1.4x-5.9 ALIGN=MIDDLE  ALT=\"y=-0.2x%5E2%2B1.4x-5.9\"   DISABLED_style= \"max-width:90%; height:auto;\" >, we can see that <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a=-0.2 ALIGN=MIDDLE  ALT=\"a=-0.2\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b=1.4 ALIGN=MIDDLE  ALT=\"b=1.4\"   DISABLED_style= \"max-width:90%; height:auto;\" >, and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=c=-5.9 ALIGN=MIDDLE  ALT=\"c=-5.9\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=%28-%281.4%29%29%2F%282%28-0.2%29%29 ALIGN=MIDDLE  ALT=\"x=%28-%281.4%29%29%2F%282%28-0.2%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Plug in <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a=-0.2 ALIGN=MIDDLE  ALT=\"a=-0.2\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b=1.4 ALIGN=MIDDLE  ALT=\"b=1.4\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=%28-%281.4%29%29%2F%28-0.4%29 ALIGN=MIDDLE  ALT=\"x=%28-%281.4%29%29%2F%28-0.4%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply 2 and -0.2 to get -0.4\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=3.5 ALIGN=MIDDLE  ALT=\"x=3.5\"   DISABLED_style= \"max-width:90%; height:auto;\" > Divide -1.4 and -0.4 to get 3.5\r<BR>\n" );
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document.write( "So the x-coordinate of the vertex is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=3.5 ALIGN=MIDDLE  ALT=\"x=3.5\"   DISABLED_style= \"max-width:90%; height:auto;\" >. Note: this means that the axis of symmetry is also <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=3.5 ALIGN=MIDDLE  ALT=\"x=3.5\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "Now that we know the x-coordinate of the vertex, we can use it to find the y-coordinate of the vertex.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=-0.2x%5E2%2B1.4x-5.9 ALIGN=MIDDLE  ALT=\"y=-0.2x%5E2%2B1.4x-5.9\"   DISABLED_style= \"max-width:90%; height:auto;\" > Start with the given equation.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=-0.2%2A%283.5%29%5E2%2B1.4%283.5%29-5.9 ALIGN=MIDDLE  ALT=\"y=-0.2%2A%283.5%29%5E2%2B1.4%283.5%29-5.9\"   DISABLED_style= \"max-width:90%; height:auto;\" > Plug in <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=3.5 ALIGN=MIDDLE  ALT=\"x=3.5\"   DISABLED_style= \"max-width:90%; height:auto;\" > \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=-0.2%2812.25%29%2B1.4%283.5%29-5.9 ALIGN=MIDDLE  ALT=\"y=-0.2%2812.25%29%2B1.4%283.5%29-5.9\"   DISABLED_style= \"max-width:90%; height:auto;\" > Square <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3.5 ALIGN=MIDDLE  ALT=\"3.5\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=12.25 ALIGN=MIDDLE  ALT=\"12.25\"   DISABLED_style= \"max-width:90%; height:auto;\" >.  \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=-2.45%2B1.4%283.5%29-5.9 ALIGN=MIDDLE  ALT=\"y=-2.45%2B1.4%283.5%29-5.9\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-0.2 ALIGN=MIDDLE  ALT=\"-0.2\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=12.25 ALIGN=MIDDLE  ALT=\"12.25\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-2.45 ALIGN=MIDDLE  ALT=\"-2.45\"   DISABLED_style= \"max-width:90%; height:auto;\" >.  \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=-2.45%2B4.9-5.9 ALIGN=MIDDLE  ALT=\"y=-2.45%2B4.9-5.9\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1.4 ALIGN=MIDDLE  ALT=\"1.4\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3.5 ALIGN=MIDDLE  ALT=\"3.5\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4.9 ALIGN=MIDDLE  ALT=\"4.9\"   DISABLED_style= \"max-width:90%; height:auto;\" >.  \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=2.45-5.9 ALIGN=MIDDLE  ALT=\"y=2.45-5.9\"   DISABLED_style= \"max-width:90%; height:auto;\" > Add <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-2.45 ALIGN=MIDDLE  ALT=\"-2.45\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4.9 ALIGN=MIDDLE  ALT=\"4.9\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2.45 ALIGN=MIDDLE  ALT=\"2.45\"   DISABLED_style= \"max-width:90%; height:auto;\" >.  \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=-3.45 ALIGN=MIDDLE  ALT=\"y=-3.45\"   DISABLED_style= \"max-width:90%; height:auto;\" > Subtract <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5.9 ALIGN=MIDDLE  ALT=\"5.9\"   DISABLED_style= \"max-width:90%; height:auto;\" > from <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2.45 ALIGN=MIDDLE  ALT=\"2.45\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-3.45 ALIGN=MIDDLE  ALT=\"-3.45\"   DISABLED_style= \"max-width:90%; height:auto;\" >.  \r<BR>\n" );
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document.write( "So the y-coordinate of the vertex is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=-3.45 ALIGN=MIDDLE  ALT=\"y=-3.45\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "This means that the vertex is <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \left(3.5,-3.45\right)\">.<BR>\n" );
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