document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=49111>Question 49111</A>: <I><SPAN STYLE=\"word-break: break-all;\"> if the parabola y-2=a(x-3)exponent 2 goes through the point (2,0), what is the value of a ? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #32550 by </B><A HREF=/tutors/aboutme.mpl?userid=Born2TeachMath><B>Born2TeachMath(20)</B></A><img src=\"/images/stars/stars-06.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Born2TeachMath><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=32550\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Given the parabola y-2 = a(x-3)^2 goes through the point (2, 0), this means that algebraically, if you plug in x = 2 and y = 0, then the equation will be true (the left side will equal the right side).  Therefore, to find the value of \"a\", plug in x = 2 and y = 0 and then just solve for \"a\"\r<BR>\n" );
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document.write( "y-2 = a(x-3)^2<BR>\n" );
document.write( "0-2 = a(2-3)^2<BR>\n" );
document.write( "-2 = a(-1)^2<BR>\n" );
document.write( "-2 = a(1) since (-1)^2 = 1<BR>\n" );
document.write( "-2 = a  since a(1) = a\r<BR>\n" );
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document.write( "So the value of a needed to make the parabola y-2 = a(x-3)^2 pass through the point (2, 0) is a = -2\r<BR>\n" );
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document.write( "Remember - the key here is to know that if a given point \"lies on a graph\", the the values of the point plugged into the equaiont for the graph makes the left side equal to the right side when both are evaluated!  </SPAN>\n" );
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