document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=155148>Question 155148</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Given that a quadratic goes through the points (-1,0), (0.67,0), and (0,-2), find the quadratic that goes through the points and find the solutions. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #114223 by </B><A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><B>jim_thompson5910(35256)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><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=114223\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <BR>\n" );
document.write( "Since there are two real solutions, this means that the discriminant is greater than zero. Since the x-intercepts are (-1,0) and (0.67,0) this means that the solutions are <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=-1 ALIGN=MIDDLE  ALT=\"x=-1\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=0.67 ALIGN=MIDDLE  ALT=\"x=0.67\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=-1 ALIGN=MIDDLE  ALT=\"x=-1\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=0.67 ALIGN=MIDDLE  ALT=\"x=0.67\"   DISABLED_style= \"max-width:90%; height:auto;\" > Start with the given solutions\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2B1=0 ALIGN=MIDDLE  ALT=\"x%2B1=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x-0.67=0 ALIGN=MIDDLE  ALT=\"x-0.67=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > Get every term to the left side\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%28x%2B1%29%28x-0.67%29=0 ALIGN=MIDDLE  ALT=\"a%28x%2B1%29%28x-0.67%29=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > Use the zero product property to join the two equations. I'm introducing the term \"a\" to make sure that the quadratic goes through the point (0,-2)\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%28x%5E2-0.67x%2Bx-0.67%29=0 ALIGN=MIDDLE  ALT=\"a%28x%5E2-0.67x%2Bx-0.67%29=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > FOIL\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%28x%5E2%2B0.33x-0.67%29=0 ALIGN=MIDDLE  ALT=\"a%28x%5E2%2B0.33x-0.67%29=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > Combine like terms.\r<BR>\n" );
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document.write( "So the equation becomes <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=a%28x%5E2%2B0.33x-0.67%29 ALIGN=MIDDLE  ALT=\"y=a%28x%5E2%2B0.33x-0.67%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-2=a%280%5E2%2B0.33%280%29-0.67%29 ALIGN=MIDDLE  ALT=\"-2=a%280%5E2%2B0.33%280%29-0.67%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Plug in <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=0 ALIGN=MIDDLE  ALT=\"x=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=-2 ALIGN=MIDDLE  ALT=\"y=-2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-2=a%28-0.67%29 ALIGN=MIDDLE  ALT=\"-2=a%28-0.67%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply and simplify. Notice how everything cancels out but the \"0.67\"\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-2=a%28-0.67%29 ALIGN=MIDDLE  ALT=\"-2=a%28-0.67%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply and simplify. Notice how everything cancels out but the \"0.67\"\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3=a ALIGN=MIDDLE  ALT=\"3=a\"   DISABLED_style= \"max-width:90%; height:auto;\" > Divide both sides by -0.67 to isolate \"a\"\r<BR>\n" );
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document.write( "So the constant is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a=3 ALIGN=MIDDLE  ALT=\"a=3\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=3%28x%5E2%2B0.33x-0.67%29 ALIGN=MIDDLE  ALT=\"y=3%28x%5E2%2B0.33x-0.67%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Plug in <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a=3 ALIGN=MIDDLE  ALT=\"a=3\"   DISABLED_style= \"max-width:90%; height:auto;\" > into the equation\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=3%28x%5E2%29%2B3%280.33x%29-3%280.67%29 ALIGN=MIDDLE  ALT=\"y=3%28x%5E2%29%2B3%280.33x%29-3%280.67%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Distribute\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=3x%5E2%2Bx-2 ALIGN=MIDDLE  ALT=\"y=3x%5E2%2Bx-2\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply\r<BR>\n" );
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document.write( "So the equation that goes through the three points is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=3x%5E2%2Bx-2 ALIGN=MIDDLE  ALT=\"y=3x%5E2%2Bx-2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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