document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=965749>Question 965749</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Difference between linear equation and quadratic equation<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #590270 by </B><A HREF=/tutors/aboutme.mpl?userid=Theo><B>Theo(13342)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Theo><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=Theo><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=590270\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> the graph of a linear eqution will be a straight line.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "the graph of a quadratic equation will look like the top part of an umbrella.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "the linear equation can be a constant or it can be a variable with an exponent of 1.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "the exponent of 1 is usually not shown because it is implied.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "x is the same as x^1, and is usually shown as x, although it can be shown as x^1 when necessary.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "some examples of a linear equation.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "y = 1<BR>\n" );
document.write( "y = x<BR>\n" );
document.write( "y = x + 1\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "the quadratic equation has to have a varible with an exponent of 2, and any other variable in the equation has to be positive and less than 2.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "some examples of quadratic equations.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "x^2<BR>\n" );
document.write( "x^2 + x<BR>\n" );
document.write( "x^2 + x + 1\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "both linear equations and quadratic equatons are polynomials which means that the exponent of any variable in the equation must be a positive integer.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "their graphs will be continuous from start to finish.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "here's a graph of y = x + 1\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28400%2C400%2C-10%2C10%2C-10%2C10%2Cx%2B1%29 ALIGN=MIDDLE  ALT=\"graph%28400%2C400%2C-10%2C10%2C-10%2C10%2Cx%2B1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "here's a graph of y = x^2 + x + 1\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28400%2C400%2C-10%2C10%2C-10%2C10%2Cx%5E2%2Bx%2B1%29 ALIGN=MIDDLE  ALT=\"graph%28400%2C400%2C-10%2C10%2C-10%2C10%2Cx%5E2%2Bx%2B1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "here's a graph of y = x^2 + x^-1 + 1\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28400%2C400%2C-10%2C10%2C-10%2C10%2Cx%5E2%2Bx%5E-1%2B1%29 ALIGN=MIDDLE  ALT=\"graph%28400%2C400%2C-10%2C10%2C-10%2C10%2Cx%5E2%2Bx%5E-1%2B1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "that last graph is not a polynomial because it contains a variable with an exponent that is not a positive integer.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "you can see that it is also not continuous because there is a break in the graph at x = 0 where the value of y is undefined because you have a division by 0 when x is equal to 0.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "x^-1 is the same a 1/x.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "when x is equal to 0, that becomes 1/0.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "the first 2 graphs are polynopmials.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "the last graph is not.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );