document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1120589>Question 1120589</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Find the domain and the range of the quadratic function whose minimum value is 15 at x=&#8722;5, Would I just plug in 15 for x? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #736255 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=736255\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font face=\"Times New Roman\" size=\"+2\">\r<BR>\n" );
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document.write( "The domain of a function is the set of all numbers for which the function is defined.  For all polynomial functions, a classification that includes all quadratic functions, the domain is all real numbers, i.e.:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ \text{dom}f\ =\ \{x\ \in\ \mathbb{R}\}\">\r<BR>\n" );
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document.write( "The range of a function is the set of all possible values for a function evaluated at all possible values of the domain.  For all polynomial functions of even degree, a classification that includes all quadratic functions, there is an absolute minimum value (for those polynomial functions where the lead coefficient is positive) or an absolute maximum value (lead coefficient negative).  In the case of your example, -5 is the absolute minimum value, and the function does not have a maximum value.  That means the range is the set of all real values that are greater than or equal to -5.  So for <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large y\ =\ f(x)\">:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ \text{rng}f\ =\ \{y\ \in\ \mathbb{R}\ |\ -5\ \leq\ y\ <\ \infty\}\"><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" );
document.write( "My calculator said it, I believe it, that settles it<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large \ \\r\"> </SPAN>\n" );
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