document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=398754>Question 398754</A>: <I><SPAN STYLE=\"word-break: break-all;\"> the vertex form equation of parabola identify coordinate v(h,k) <BR>\n" );
document.write( "1)y=2x^2+32x+125<BR>\n" );
document.write( "2)x^2-6x+y+9=0 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #282489 by </B><A HREF=/tutors/aboutme.mpl?userid=lwsshak3><B>lwsshak3(11628)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=lwsshak3><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=282489\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> the vertex form equation of parabola identify coordinate v(h,k)<BR>\n" );
document.write( "1)y=2x^2+32x+125<BR>\n" );
document.write( "2)x^2-6x+y+9=0\r<BR>\n" );
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document.write( "To identify the coordinates of a parabola, you can write the equation in this form: y=(x-h)^2+k, (h,k) being the (x,y) coordinates of the vertex.  You must complete the square to do this.\r<BR>\n" );
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document.write( "(1)y=2x^2+32x+125<BR>\n" );
document.write( "completing the square<BR>\n" );
document.write( "factor out 2<BR>\n" );
document.write( "y=2(x^2+16x+64)+125-128 (we added 2*64 to complete the square,so we must add -128 to even things out<BR>\n" );
document.write( "y=2(x+8)^2-3<BR>\n" );
document.write( "vertex: (-8,-3)\r<BR>\n" );
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document.write( "(2)x^2-6x+y+9=0<BR>\n" );
document.write( " y=-(x^2-6x+ )-9<BR>\n" );
document.write( "y=-(x^2-6x+9)-9+9  (we added -9 to complete the square,so we must add 9 to even<BR>\n" );
document.write( " things out<BR>\n" );
document.write( "y=-(x-3)^2)+0<BR>\n" );
document.write( "vertex: (3,0)\r<BR>\n" );
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document.write( "Another method for finding the coordinates of the vertex is to use the formula:<BR>\n" );
document.write( "x=-b/2a,a being the coefficient of the x^2-term, and b the coefficient of the x-term. In equation (1) above, x=-16/2=-8, then substitute this value for x in the equation to find y=128-256+125=-3.  If you are just trying to find the coordinates of the vertex, this might be a more simple way, but the first method will yield more information about the parabola.You should learn both ways.\r<BR>\n" );
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document.write( "see the following graphs of the two parabola equations:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+graph%28+300%2C+200%2C+-10%2C+5%2C+-6%2C+6%2C+2x%5E2%2B32x%2B125%2C-%28x%5E2-6x%2B9+%29%29 ALIGN=MIDDLE  ALT=\"+graph%28+300%2C+200%2C+-10%2C+5%2C+-6%2C+6%2C+2x%5E2%2B32x%2B125%2C-%28x%5E2-6x%2B9+%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( " </SPAN>\n" );
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