document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1075366>Question 1075366</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Given the graph below, write the radical function for f(x).<BR>\n" );
document.write( "These are the coordinates that I took from my homework:<BR>\n" );
document.write( "(-2,3)(-1,2)(2,1)(7,0)\r<BR>\n" );
document.write( "\n" );
document.write( "I am sorry if I don't have a graph to place on this website, but radical function means A function that contains a radical expression with the independent variable in the radicand. Also a radicand is the number or expression inside a radical symbol.  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #690059 by </B><A HREF=/tutors/aboutme.mpl?userid=KMST><B>KMST(5328)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=KMST><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=KMST><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=690059\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> If your graph has only those 4 points,<BR>\n" );
document.write( "it is a cumbersome problem.<BR>\n" );
document.write( "I would start with <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=ay%5E2%2Bby%2Bc ALIGN=MIDDLE  ALT=\"x=ay%5E2%2Bby%2Bc\"   DISABLED_style= \"max-width:90%; height:auto;\" > ,<BR>\n" );
document.write( "would solve for a, b, and c,<BR>\n" );
document.write( "and then would solve for y.<BR>\n" );
document.write( "Substituting the coordinates of (7,0),<BR>\n" );
document.write( "you get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=7=c ALIGN=MIDDLE  ALT=\"7=c\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( "Point (2,1) gives you<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2=a%2Bb%2Bc=a%2Bb%2B7 ALIGN=MIDDLE  ALT=\"2=a%2Bb%2Bc=a%2Bb%2B7\"   DISABLED_style= \"max-width:90%; height:auto;\" > ---> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%2Bb=-5 ALIGN=MIDDLE  ALT=\"a%2Bb=-5\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( "Point (-1,2) gives you<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-1=4a%2B2b%2B7 ALIGN=MIDDLE  ALT=\"-1=4a%2B2b%2B7\"   DISABLED_style= \"max-width:90%; height:auto;\" >---><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4a%2B2b=-8 ALIGN=MIDDLE  ALT=\"4a%2B2b=-8\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Solving <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=system%28a%2Bb=-5%2C4a%2B2b=-8%29 ALIGN=MIDDLE  ALT=\"system%28a%2Bb=-5%2C4a%2B2b=-8%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > , you get<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a=1 ALIGN=MIDDLE  ALT=\"a=1\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b=-6 ALIGN=MIDDLE  ALT=\"b=-6\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( "So, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=y%5E2-6y%2B7 ALIGN=MIDDLE  ALT=\"x=y%5E2-6y%2B7\"   DISABLED_style= \"max-width:90%; height:auto;\" > fits 3 of the points.<BR>\n" );
document.write( "The fourth point confirms it.<BR>\n" );
document.write( "Solving <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%5E2-6y%2B7-x=0 ALIGN=MIDDLE  ALT=\"y%5E2-6y%2B7-x=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > for y, you get<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=%286+%2B-+sqrt%2836%2B4%28x-7%29%29%29%2F2 ALIGN=MIDDLE  ALT=\"y=%286+%2B-+sqrt%2836%2B4%28x-7%29%29%29%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" > ,<BR>\n" );
document.write( "which simplifies to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=3+%2B-+sqrt%28x%2B2%29 ALIGN=MIDDLE  ALT=\"y=3+%2B-+sqrt%28x%2B2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( "That is 2 choices.<BR>\n" );
document.write( "Your function increases as x increases, so it is<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29=3%2Bsqrt%28x%2B2%29 ALIGN=MIDDLE  ALT=\"f%28x%29=3%2Bsqrt%28x%2B2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( " <BR>\n" );
document.write( "If your graph is a continuous curve that looks like this:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=drawing%28300%2C300%2C-5%2C10%2C-5%2C10%2Cgrid%281%29%2C%0D%0Agraph%28300%2C300%2C-5%2C10%2C-5%2C10%2C3%2B+sqrt%28x%2B2%29%29%0D%0A%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "you would think that it looks just like <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=g%28x%29=sqrt%28x%29 ALIGN=MIDDLE  ALT=\"g%28x%29=sqrt%28x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > ,<BR>\n" );
document.write( "but translated 2 units to the left and 3 units up.<BR>\n" );
document.write( "That would make it <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29=3%2Bsqrt%28x%2B2%29 ALIGN=MIDDLE  ALT=\"f%28x%29=3%2Bsqrt%28x%2B2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( "I would bet that is what the teacher wants, and if so,<BR>\n" );
document.write( "there should be something to tell you that the function was a transformed <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=sqrt%28x%29 ALIGN=MIDDLE  ALT=\"y=sqrt%28x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( " <BR>\n" );
document.write( "At least you should think there is<BR>\n" );
document.write( "an <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2B2 ALIGN=MIDDLE  ALT=\"x%2B2\"   DISABLED_style= \"max-width:90%; height:auto;\" > inside the squate root,<BR>\n" );
document.write( "because the function is not defined for <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%3C-2 ALIGN=MIDDLE  ALT=\"x%3C-2\"   DISABLED_style= \"max-width:90%; height:auto;\" > <---> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2B2%3C0 ALIGN=MIDDLE  ALT=\"x%2B2%3C0\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( "Then you would also think there is a positive coefficient<BR>\n" );
document.write( "multiplying the square root, because y increases with x,<BR>\n" );
document.write( "and a 3 added to the square root term,<BR>\n" );
document.write( "because the graph starts at y=3. </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );