document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1198223>Question 1198223</A>: <I><SPAN STYLE=\"word-break: break-all;\"> hi please help me to answer this general to standard form. y = 2x² - 4x + 1<BR>\n" );
document.write( "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 #831779 by </B><A HREF=/tutors/aboutme.mpl?userid=math_tutor2020><B>math_tutor2020(3817)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=math_tutor2020><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=831779\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font color=black size=3><BR>\n" );
document.write( "Given equation: y = 2x^2-4x+1\r<BR>\n" );
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document.write( "It is of the form y = ax^2+bx+c<BR>\n" );
document.write( "a = 2<BR>\n" );
document.write( "b = -4<BR>\n" );
document.write( "c = 1\r<BR>\n" );
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document.write( "Use the first two values to find that<BR>\n" );
document.write( "h = -b/(2a)<BR>\n" );
document.write( "h = -(-4)/(2*2)<BR>\n" );
document.write( "h = 1<BR>\n" );
document.write( "This is the x coordinate of the vertex (h,k)\r<BR>\n" );
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document.write( "Plug this into the given equation to find the y coordinate of the vertex.<BR>\n" );
document.write( "y = 2x^2-4x+1<BR>\n" );
document.write( "y = 2(1)^2-4(1)+1<BR>\n" );
document.write( "y = -1<BR>\n" );
document.write( "Therefore k = -1 is the y coordinate of the vertex (h,k)\r<BR>\n" );
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document.write( "Vertex = (h,k) = (1,-1)<BR>\n" );
document.write( "This represents the lowest point on the parabola.<BR>\n" );
document.write( "We know the parabola opens upward because a > 0.\r<BR>\n" );
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document.write( "Summary:<BR>\n" );
document.write( "a = 2<BR>\n" );
document.write( "h = 1<BR>\n" );
document.write( "k = -1<BR>\n" );
document.write( "Vertex form y = a(x-h)^2+k then leads to <font color=red>y = 2(x-1)^2-1</font>\r<BR>\n" );
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document.write( "Graph:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=drawing%28500%2C500%2C-7%2C7%2C-7%2C7%2C%0D%0Agraph%28500%2C500%2C-7%2C7%2C-7%2C7%2C0%2C2x%5E2-4x%2B1%29%2C%0D%0Acircle%281%2C-1%2C0.1%29%2C%0D%0Acircle%281%2C-1%2C0.12%29%2C%0D%0Acircle%281%2C-1%2C0.15%29%2C%0D%0Alocate%281%2C-1%2C%22%281%2C-1%29%22%29%0D%0A%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "I recommend using free graphing tools like Desmos and GeoGebra. <BR>\n" );
document.write( "Or you can use a TI83 or TI84 calculator (or similar).<BR>\n" );
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