document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=208012>Question 208012</A>: <I><SPAN STYLE=\"word-break: break-all;\"> could someone please tell me the answer to this question?\r<BR>\n" );
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document.write( "a parabola that opens to the right is a \r<BR>\n" );
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document.write( "radicand,function,linear equation,or relation.thanks<BR>\n" );
document.write( "hagd. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #157372 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=157372\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> a parabola that opens to the right is a relation.<BR>\n" );
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document.write( "an equation is a function if there is one and only one value of y for each x.<BR>\n" );
document.write( "otherwise it is a relation.<BR>\n" );
document.write( "when you take a parabola and turn it to the right you get 2 values of y for each x which makes it not a function which makes it a relation.<BR>\n" );
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document.write( "it is not a linear equation because a linear equation is an equation of a straight line.<BR>\n" );
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document.write( "it might be a radicand but we'll have to see how that pans out.<BR>\n" );
document.write( "a radicand is an expression under the root sign.<BR>\n" );
document.write( "if you take the square root of x, then x is the radicand because it is under the square root sign.<BR>\n" );
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document.write( "let's see what happens.<BR>\n" );
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document.write( "a quadratic equation is an equation of a parabola.<BR>\n" );
document.write( "let's take y = x^2 + 3x + 2<BR>\n" );
document.write( "graph of this equation would be:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28600%2C600%2C-5%2C5%2C-5%2C5%2Cx%5E2+%2B+3x+%2B+2%29 ALIGN=MIDDLE  ALT=\"graph%28600%2C600%2C-5%2C5%2C-5%2C5%2Cx%5E2+%2B+3x+%2B+2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "this is a parabola that opens upward.<BR>\n" );
document.write( "it is a function because there is one and only 1 value of y for each x.<BR>\n" );
document.write( "it is not a radicand because the equations is not under the root sign.<BR>\n" );
document.write( "it is not a relation because it is a function.  those are mutually exclusive.<BR>\n" );
document.write( "it is not a linear equation because it is not the equation of a straight line.<BR>\n" );
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document.write( "now let's take y = +/- <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%28%28x+%2B+.25%29%29+-+1.5%29 ALIGN=MIDDLE  ALT=\"sqrt%28%28x+%2B+.25%29%29+-+1.5%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "we got this equation by taking the previous quadratic equation of y = x^2 + 3x + 2 and solving for x and then making y = x and x = y.<BR>\n" );
document.write( "graph of this equation would be:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28600%2C600%2C-5%2C5%2C-5%2C5%2Csqrt%28x+%2B+.25%29+-+1.5%2C+-sqrt%28x+%2B+.25%29+-+1.5%2C+x%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "this is a parabola that opens to the right.<BR>\n" );
document.write( "it is not a function because there is more than 1 value of y for at least one of the x's.<BR>\n" );
document.write( "it is a relation because it is not a function.  those are mutually exclusive.  the equation is either a function or a relation, never both.<BR>\n" );
document.write( "it is not a linear eqution because it is not the equation of a straight line.<BR>\n" );
document.write( "it is not a radicand because the whole equation is not under the radical sign, only a portion of it.<BR>\n" );
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document.write( "interesting tidbit:<BR>\n" );
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document.write( "the equation of y = +/- <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%28%28x+%2B+.25%29%29+-+1.5%29 ALIGN=MIDDLE  ALT=\"sqrt%28%28x+%2B+.25%29%29+-+1.5%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > is the inverse equation of y = x^2 + 3x + 2.<BR>\n" );
document.write( "you create an inverse equation by solving for x and then inverting the x and the y which is what we did.<BR>\n" );
document.write( "this means that the equations are reflections of each other about the line y = x.<BR>\n" );
document.write( "you should be able to see this in the following graph of both equations and the line y = x<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28600%2C600%2C-5%2C5%2C-5%2C5%2Cx%5E2+%2B+3x+%2B+2%2C+x%2Csqrt%28x+%2B+.25%29+-+1.5%2C+-sqrt%28x+%2B+.25%29+-+1.5%2C+x%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "you probably didn't need to know that but since i created your right facing parabola by inverting your upward facing parabola, i thought you might be interested in the relationship that was created by doing that.<BR>\n" );
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document.write( "fyi,<BR>\n" );
document.write( "the original equation is a function but the inverse equation is a relation because of the rules of functions described earlier.  this is not always the case.  it is just the case for this equation.<BR>\n" );
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