document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=216956>Question 216956</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I am having difficulty with a question.  The question is as follows:  A parabola has an x-intercept at 2, its axis of symmetry is the line x=4, and the y-coordinate of its vertex is 6.  Determine the equation of the parabola.\r<BR>\n" );
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document.write( "I am setting up my problem as y = ax^2 + bx + c and I since x = 4, y must be 0<BR>\n" );
document.write( "o = 16 + 4 + c.  I'm confused and I don't think I am setting up the equation correctly.\r<BR>\n" );
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document.write( "Thanks - Lori </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #163789 by </B><A HREF=/tutors/aboutme.mpl?userid=ankor@dixie-net.com><B>ankor@dixie-net.com(22740)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=ankor@dixie-net.com><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/cgi-bin/show-face.mpl?user=ankor@dixie-net.com><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=163789\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> I am having difficulty with a question.<BR>\n" );
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document.write( "The question is as follows: A parabola has an x-intercept at 2, <BR>\n" );
document.write( "its axis of symmetry is the line x=4, and the y-coordinate of its vertex is 6. <BR>\n" );
document.write( "Determine the equation of the parabola.<BR>\n" );
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document.write( "I am setting up my problem as y = ax^2 + bx + c and I since x = 4, y must be 0<BR>\n" );
document.write( "Not right: the axis of symmetry is given as 4 and y coordinate as 6 so you have:<BR>\n" );
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document.write( "x = 4; y = 6 (vertex)<BR>\n" );
document.write( "(4^2)a + 4b + c = 6<BR>\n" );
document.write( "16a + 4b + c = 6<BR>\n" );
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document.write( "and the intercept<BR>\n" );
document.write( "x = 2; y = 0<BR>\n" );
document.write( "(2^2)a + 2b + c = 0<BR>\n" );
document.write( "4a + 2b + c = 0<BR>\n" );
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document.write( "Here we can reason:<BR>\n" );
document.write( " the two intercepts are equidistant from the axis of symmetry <BR>\n" );
document.write( "One intercept is +2, the axis symmetry is +4 then the other intercept is +6<BR>\n" );
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document.write( "x = 6; y = 0<BR>\n" );
document.write( "(6^2)a + 6b + c = 0<BR>\n" );
document.write( "36a + 6b + c = 0<BR>\n" );
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document.write( "Three equations to find three unknowns, a, b, c<BR>\n" );
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document.write( "use the 1st two equations to eliminate c<BR>\n" );
document.write( "16a + 4b + c = 6<BR>\n" );
document.write( " 4a + 2b + c = 0<BR>\n" );
document.write( "-------------------Subtraction eliminates c<BR>\n" );
document.write( "12a + 2b = 6<BR>\n" );
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document.write( "do the same with the 1st and 3rd equation<BR>\n" );
document.write( "36a + 6b + c = 0<BR>\n" );
document.write( "16a + 4b + c = 6<BR>\n" );
document.write( "------------------Subtraction eliminates c<BR>\n" );
document.write( "20a + 2b = -6<BR>\n" );
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document.write( "Use these two equations, and eliminate b and find a<BR>\n" );
document.write( "20a + 2b = -6<BR>\n" );
document.write( "12a + 2b = 6<BR>\n" );
document.write( "--------------Subtraction eliminates b<BR>\n" );
document.write( "8a = -12<BR>\n" );
document.write( "a = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28-12%29%2F8 ALIGN=MIDDLE  ALT=\"%28-12%29%2F8\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "a = -1.5<BR>\n" );
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document.write( "Find b using eq: 12a + 2b = 6<BR>\n" );
document.write( "12(-1.5) + 2b = 6<BR>\n" );
document.write( "-18 + 2b = 6<BR>\n" );
document.write( "2b = 6 + 18<BR>\n" );
document.write( "2b = 24<BR>\n" );
document.write( "b = 12<BR>\n" );
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document.write( "Find c using eq: 4a + 2b + c = 0<BR>\n" );
document.write( "4(-1.5) + 2(12) + c = 0<BR>\n" );
document.write( "-6 + 24 + c = 0<BR>\n" );
document.write( "18 + c = 0<BR>\n" );
document.write( "c = -18<BR>\n" );
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document.write( "The equation: y = -1.5x^2 + 12x -18 <BR>\n" );
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document.write( "Check this by graphing it<BR>\n" );
document.write( " <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+graph%28+300%2C+200%2C+-6%2C+10%2C+-4%2C+8%2C+-1.5x%5E2%2B12x-18%29+ ALIGN=MIDDLE  ALT=\"+graph%28+300%2C+200%2C+-6%2C+10%2C+-4%2C+8%2C+-1.5x%5E2%2B12x-18%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Two x intercepts at +2 and +6; vertex: 4,6. </SPAN>\n" );
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