document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=217107>Question 217107</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I am having difficulty with a question.  The problems is as follows:  A parabola has an x-intercept at 2, its axis of symmetry is the l ine x=4, and the y-coordinate of its vertex is 6.  Determone the equation of the parabola.\r<BR>\n" );
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document.write( "I am setting up my equation -   y = ax^2 + bx + c   and plugging in the numbers as follows:    y = 4a^2 + 2b + 8.  Am I on the right track?\r<BR>\n" );
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document.write( "Thanks,\r<BR>\n" );
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document.write( "Lori  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #163744 by </B><A HREF=/tutors/aboutme.mpl?userid=RAY100><B>RAY100(1637)</B></A><img src=\"/images/stars/stars-12.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=RAY100><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=163744\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> a  rough  sketch  helps,,,,,<BR>\n" );
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document.write( "On  x-y  coordinates, line  if  symmetry  is  x=4,  so  draw  a  vertical  at  +4<BR>\n" );
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document.write( "We  also  know  that  the  vertex  is  on  the  line  of  symmetry  so (4,?) is  vertex<BR>\n" );
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document.write( "But  they  give  y=6 at  vertex,,,,,therefore  vertex  is (4,6),,,might  draw  point<BR>\n" );
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document.write( "Since  x  intercept  is  2,,,(1) we  know(2,0)  is  point  on  curve,<BR>\n" );
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document.write( "(2) drawing  point  on  rough  graph,  shows  it  to  be  curve  pointing  down.<BR>\n" );
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document.write( "The  basic  eqn  is  probably  a  y  parabola  pointing  down  ,,,,,,from  sketch<BR>\n" );
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document.write( "base  eqn  is  y=x^2 +b<BR>\n" );
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document.write( "expanded  form  is (y-k) = A(x-h)^2<BR>\n" );
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document.write( "we  know  vertex is (4,6) ,,,therefore h=4,,,k=6<BR>\n" );
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document.write( "subst,,,,(y-6)=A(x-4)^2,,,,,subst (2,0)<BR>\n" );
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document.write( "{(0)-6} =A {(2)-4}^2<BR>\n" );
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document.write( "-6 =A(-2)^2<BR>\n" );
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document.write( "-6 =A(4)<BR>\n" );
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document.write( "A=-6/4 = -3/2=-1.5,,,,,,note  negative  confirms  pointing  down parabola<BR>\n" );
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document.write( "combining,,,,(y-6)=-1.5(x-4)^2,,,,,answer<BR>\n" );
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document.write( "checking,,,,(2,0),,,,(0-6) =-1.5(2-4)^2,,,-6=-1.5(-2)^2 =-1.5*4=-6,,,ok<BR>\n" );
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document.write( "and (4,6),,,,,,6-6= -1.5(4-4)^2,,,,or  0=0,,,,,ok<BR>\n" );
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document.write( "in  standard  form,,,(y-6) = -1.5(x-4)^2<BR>\n" );
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document.write( "y-6 =-1,5{x^2-8x+16) = -1.5x^2 +12x -24<BR>\n" );
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document.write( "y= -1.5x^2 +12x -18,,,,,std  form  answer<BR>\n" );
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document.write( "checking,,,vertex  x = -b/2a = -12/(2*-1.5) = +4 ,,,,,ok<BR>\n" );
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document.write( "y=-1.5(4)^2 +12(4) -18 = -24 +48-18=6,,,,ok<BR>\n" );
document.write( ".\r<BR>\n" );
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document.write( " </SPAN>\n" );
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