document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=106110>Question 106110</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The sign of the discriminant D is positive as the parabola opens upward.<BR>\n" );
document.write( "We observe the x intercepts to be –1, and 0.67<BR>\n" );
document.write( "So the function is written as y = a(x – (-1)) (x – 0.67) where ‘a’ is a constant.<BR>\n" );
document.write( "y = a (x + 1) (x – 0.67)<BR>\n" );
document.write( "The lowest point of the parabola is the vertex.<BR>\n" );
document.write( "Now the parabola passes through (- 0.16, -2)<BR>\n" );
document.write( "-2 = a( - 0.16 + 1) ( - 0.16 – 0.67)<BR>\n" );
document.write( "-2 = a(0.84) (- 0.83)<BR>\n" );
document.write( "a = -2/ (0.84)(- 0.83)<BR>\n" );
document.write( "a = 2.87<BR>\n" );
document.write( "Thus the quadratic equation is y = 2.87 ( x + 1) (x – 0.67)<BR>\n" );
document.write( "Or y = 2.87 (x2 + 0.33x – 0.67)<BR>\n" );
document.write( "The quadratic equation is 2.87 ( x2 + 0.33x – 0.67 ) = y<BR>\n" );
document.write( "To solve for x, we equate y to 0.<BR>\n" );
document.write( "x2 + 0.33x – 0.67 = 0<BR>\n" );
document.write( "x2 + 0.33x – 0.67 = 0<BR>\n" );
document.write( "x2 + x – 0.67 x – 0.67 = 0<BR>\n" );
document.write( "x (x + 1) – 0.67 ( x + 1) = 0<BR>\n" );
document.write( "(x + 1) (x – 0.67) = 0<BR>\n" );
document.write( "X + 1 = 0 or x – 0.67 = 0<BR>\n" );
document.write( "X = -1 or x = 0.67<BR>\n" );
document.write( "The solution is x = -1 or x = 0.67\r<BR>\n" );
document.write( "\n" );
document.write( "This is a discussion group question. One of the girls on my team came up with this but I can't figure out where she got the 0.33x. I thought I was getting it but now I am confused. Can you explain this? Please, Please! </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #77200 by </B><A HREF=/tutors/aboutme.mpl?userid=Fombitz><B>Fombitz(32388)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Fombitz><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=Fombitz><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=77200\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Look at this part of the discussion when you multiplied the factors together. <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=2.87%28x%2B1%29%28x-0.67%29 ALIGN=MIDDLE  ALT=\"y=2.87%28x%2B1%29%28x-0.67%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Use the FOIL method (First Outer Inner Last)<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%2B1%29%28x-0.67%29=x%2Ax%2Bx%2A%28-0.67%29%2B%281%29x%2B%281%29%28-0.67%29 ALIGN=MIDDLE  ALT=\"%28x%2B1%29%28x-0.67%29=x%2Ax%2Bx%2A%28-0.67%29%2B%281%29x%2B%281%29%28-0.67%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%2B1%29%28x-0.67%29=x%5E2%2Bx%2Ahighlight%28%281-0.67%29%29-0.67 ALIGN=MIDDLE  ALT=\"%28x%2B1%29%28x-0.67%29=x%5E2%2Bx%2Ahighlight%28%281-0.67%29%29-0.67\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%2B1%29%28x-0.67%29=x%5E2%2Bhighlight%280.33%29x-0.67 ALIGN=MIDDLE  ALT=\"%28x%2B1%29%28x-0.67%29=x%5E2%2Bhighlight%280.33%29x-0.67\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "I hope this answers your question.  </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );