document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=190301>Question 190301</A>: <I><SPAN STYLE=\"word-break: break-all;\"> What is the domain of f, range of f, vertex, axis of symmetry, x-intercept (s), y-intercept, determine whether it has a minimum or a maximum value and state that value for f(x)=x^2+x-2\r<BR>\n" );
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document.write( "PLZZZZ help me in STRUGGLING! </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #142822 by </B><A HREF=/tutors/aboutme.mpl?userid=solver91311><B>solver91311(24713)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=solver91311><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=solver91311><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=142822\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font face=\"Garamond\" size=\"+2\">\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ f(x) = x^2 + x - 2 \"> \r<BR>\n" );
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document.write( "Since there are no real number values for which this function is undefined the domain is all real numbers or <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE (-\infty,\infty)\">.\r<BR>\n" );
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document.write( "Since this is a quadratic polynomial, the graph is a parabola.  Since the lead coefficient is positive, the parabola opens upward.  Let's table discussion of the Range until we have identified the vertex.\r<BR>\n" );
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document.write( "The <i>x</i>-coordinate of the vertex of a parabola described by a function in the form:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ \phi(x) = ax^2 + bx + c \">\r<BR>\n" );
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document.write( "is given by: <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE x_V = \frac{-b}{2a}\">\r<BR>\n" );
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document.write( "so for your function: <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE x_V = \frac{-1}{2(1)} = -\frac{1}{2}\">\r<BR>\n" );
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document.write( "The <i>y</i>-coordinate of the vertex of such a parabola is given by\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ y_V\ =\ f(x_V)\ =\ \left(-\frac{1}{2}\right)^2 - \left(\frac{1}{2}\right) - 2 = \frac{1}{4} - \frac{1}{2} - 2 = -\frac{9}{4}\">\r<BR>\n" );
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document.write( "So the vertex is the point <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \left(-\frac{1}{2},-\frac{9}{4}\right)\">\r<BR>\n" );
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document.write( "Since this is a parabola opening upward, the <i>y</i>-coordinate of the vertex represents the minimum value of the function.  And there is no maximum value, so we can now define the range as [<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE -\frac{9}{4}\">,<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \infty\">).  This also answers the question about whether there is a minimum or maximum -- and what the value of the minimum is.\r<BR>\n" );
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document.write( "The axis of symmetry is the vertical line defined by the equation <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE x = a\"> where <i>a</i> is the value of the <i>x</i>-coordinate of the vertex, so:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ x = -\frac{1}{2}\">\r<BR>\n" );
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document.write( "The <i>y</i>-intercept is the value of the function when <i>x</i> equals zero, so:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ f(0) = (0)^2 + (0) - 2 =-2\"> \r<BR>\n" );
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document.write( "The <i>x</i>-intercepts are the values of <i>x</i> that make the value of the function equal zero, so:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ x^2 + x - 2 = 0\"> \r<BR>\n" );
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document.write( "The trinomial factors, so:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ (x + 2)(x - 1) = 0\">\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ x_1 = -2\">\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ x_2 = 1\">\r<BR>\n" );
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document.write( "John<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE e^{i\pi} + 1 = 0\"><BR>\n" );
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