document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=949629>Question 949629</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Hello! I need to find the range of a quadratic equation, which is 2x^2+ -2x + 3 = 0<BR>\n" );
document.write( "Could you please help me?? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #579776 by </B><A HREF=/tutors/aboutme.mpl?userid=josgarithmetic><B>josgarithmetic(39627)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=josgarithmetic><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=579776\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Above the vertex.  Find the minimum y value, \"k\", in the standard form equation.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x%5E2%2B%28-2x%29%2B3=0 ALIGN=MIDDLE  ALT=\"2x%5E2%2B%28-2x%29%2B3=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x%5E2-2x%2B3=0 ALIGN=MIDDLE  ALT=\"2x%5E2-2x%2B3=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%28x%5E2-x%2B3%2F2%29=0 ALIGN=MIDDLE  ALT=\"2%28x%5E2-x%2B3%2F2%29=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >,  ---------------- <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%281%2F2%29%5E2 ALIGN=MIDDLE  ALT=\"%281%2F2%29%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > will complete the square.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight_green%282%28x-1%2F2%29%5E2%2B5%2F2=0%29 ALIGN=MIDDLE  ALT=\"highlight_green%282%28x-1%2F2%29%5E2%2B5%2F2=0%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Actually, \"range of the quadratic equation\" is wrong.  The solution process just given<BR>\n" );
document.write( "(although missing some arithmetic steps) is the function equated to 0, allowing you<BR>\n" );
document.write( "to see the vertex of the function, which is read directly from the equation to be<BR>\n" );
document.write( "(1/2, 5/2).\r<BR>\n" );
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document.write( "The EQUATION can be solved easily for the x values, which are the ROOTS or ZEROS of<BR>\n" );
document.write( "the quadratic function.  The RANGE of the function from which the equation comes is<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%285%2F2%3Cy%29 ALIGN=MIDDLE  ALT=\"highlight%285%2F2%3Cy%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
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