document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=238497>Question 238497</A>: <I><SPAN STYLE=\"word-break: break-all;\"> f(x)=x^2+4x-45<BR>\n" );
document.write( "Does the graph of f open up or down.<BR>\n" );
document.write( "What is the vertex (h,k) of f<BR>\n" );
document.write( "What is the axis of symmetry<BR>\n" );
document.write( "What are the intercepts<BR>\n" );
document.write( "What is the domain of f<BR>\n" );
document.write( "What is the range of f<BR>\n" );
document.write( "on what interval f is decreasing<BR>\n" );
document.write( "On what interval f is increasing </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #175266 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=175266\">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\ +\ 4x\ -\ 45\">\r<BR>\n" );
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document.write( "is a parabola of the form \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ ax^2\ +\ bx\ +\ c\">\r<BR>\n" );
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document.write( "The lead coefficient is positive so the parabola opens upward.\r<BR>\n" );
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document.write( "The <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large x\">-coordinate of the vertex is given by <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large -\frac{b}{2a}\">\r<BR>\n" );
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document.write( "Then obviously the <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large y\">-coordinate of the vertex must be <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large f\left(\frac{b}{2a}\right)\">\r<BR>\n" );
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document.write( "The axis of symmetry is the vertical line <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large x\ =\ -\frac{b}{2a}\">\r<BR>\n" );
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document.write( "The <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large x\">-intercepts, if any exist, are the values of <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large x\"> that satisfy <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?f(x)\ =\ 0\">\r<BR>\n" );
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document.write( "The <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large y\">-intercept is found by evaluating <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?f(0)\">\r<BR>\n" );
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document.write( "The domain of any polynomial function is all real numbers.  The range of a quadratic polynomial in the form\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ ax^2\ +\ bx\ +\ c\">\r<BR>\n" );
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document.write( "that opens upward is <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large \{y\,|\,y\,\in\,\R,\ y\ \geq\ f\left(\frac{b}{2a}\right)\}\">\r<BR>\n" );
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document.write( "A parabola that opens upward is increasing to the right of the vertex, that is to say the interval <font size=\"+3\">[<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large -\frac{b}{2a},\infty\">)<font size=\"+2\">\r<BR>\n" );
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document.write( "Quite obviously the decreasing interval is <font size=\"+3\">(<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large -\infty,-\frac{b}{2a}\">]<font size=\"+2\">\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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