document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=179180>Question 179180</A>This question is from textbook <A HREF=http://www.amazon.com/exec/obidos/ASIN/9780131572256/algebrahomeworkh>College Mathematics</A><BR>\n" );
document.write( ": <I><SPAN STYLE=\"word-break: break-all;\"> I am looking for the domain and the range for the equation:  x^2+y = 10\r<BR>\n" );
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document.write( "I thought that the square root of a negative number was imaginary and, as such we could not have a function from this equation.  Apparently, this is not correct.  Can you please explain what are and how to find the domain and range here? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #134133 by </B><A HREF=/tutors/aboutme.mpl?userid=edjones><B>edjones(8007)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=edjones><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=edjones><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=134133\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> y=ax^2+bx+c the form of a quadratic equation.<BR>\n" );
document.write( "y=-x^2+10<BR>\n" );
document.write( "a=-1, b=0 c=10<BR>\n" );
document.write( "a is negative so the parabla has a maximum (opens downward).<BR>\n" );
document.write( "The domain (of x) is all real numbers.<BR>\n" );
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document.write( "The maximum is (-b^2-4ac)/4a<BR>\n" );
document.write( "(-0^2-(4*-1*10))/4<BR>\n" );
document.write( "=40/4=10<BR>\n" );
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document.write( "The range (for y) is 10 to, but not including, -infinity or [10, -infinity)<BR>\n" );
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document.write( "Ed<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28500%2C500%2C-10%2C10%2C-12%2C12%2C10-x%5E2%29 ALIGN=MIDDLE  ALT=\"graph%28500%2C500%2C-10%2C10%2C-12%2C12%2C10-x%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
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