document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=7087>Question 7087</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Please help me. I need to know how to compute the intercepts of a quadratic function, and In case of a quadratic function, why are there two x-intercepts and one y-intercept? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #3878 by </B><A HREF=/tutors/aboutme.mpl?userid=Earlsdon><B>Earlsdon(6294)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Earlsdon><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=3878\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> If you were to graph a quadratic function, you would see that it results in a parabola that either opens upwards (positive x^2 coefficient) or downwards (negative x^2 coefficient).  From the graph you can readily see that the parabola crosses the y-axis only once.  But, depending on the sign of the x^2 coefficient and/or the value of the constant term, the parabola may or may not cross the x-axis.<BR>\n" );
document.write( "If the parabola does cross the x-axis, it will cross in two places and the function will have two real roots.<BR>\n" );
document.write( "If the parabola does not cross the x-axis, then the function will have two complex roots.<BR>\n" );
document.write( "A couple of examples should illustrate these ideas:\r<BR>\n" );
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document.write( "1) Quadratic functions with two real roots: 1) y=x^2-2  and 2) y = -x^2+2\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28300%2C200%2C-5%2C5%2C-10%2C10%2Cx%5E2-2%29 ALIGN=MIDDLE  ALT=\"graph%28300%2C200%2C-5%2C5%2C-10%2C10%2Cx%5E2-2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28300%2C200%2C-5%2C5%2C-10%2C10%2C-x%5E2%2B2%29 ALIGN=MIDDLE  ALT=\"graph%28300%2C200%2C-5%2C5%2C-10%2C10%2C-x%5E2%2B2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "1) Quadratic functions with two complex roots: 1) y=x^2+2  and 2) y=-x^2-2\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28300%2C200%2C-5%2C5%2C-10%2C10%2Cx%5E2%2B2%29 ALIGN=MIDDLE  ALT=\"graph%28300%2C200%2C-5%2C5%2C-10%2C10%2Cx%5E2%2B2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28300%2C200%2C-5%2C5%2C-10%2C10%2C-x%5E2-2%29 ALIGN=MIDDLE  ALT=\"graph%28300%2C200%2C-5%2C5%2C-10%2C10%2C-x%5E2-2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Finding the roots without graphing the function can be done in several different ways.  The best method to use depends on how the function is written.\r<BR>\n" );
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document.write( "Some of the methods are:\r<BR>\n" );
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document.write( "1.Factoring.<BR>\n" );
document.write( "2.Completing the square.<BR>\n" );
document.write( "3.Using the quadratic formula, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=%28-b%2B-sqrt%28b%5E2-4ac%29%29%2F%282a%29 ALIGN=MIDDLE  ALT=\"x=%28-b%2B-sqrt%28b%5E2-4ac%29%29%2F%282a%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "Method 3. will always work.\r<BR>\n" );
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