document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=73027>Question 73027</A>: <I><SPAN STYLE=\"word-break: break-all;\"> When it says 'vertically stretch by a factor of.. , or vertically compress by a factor of.. , 'horizontally stretch by a factor of.. , or horizontally compress by a factor of.. ' is there some sort of calculation to use this factor and find additional points on the graph?  I'm in section 3.1, starting with problem number 19.  I understand the transformation processes of graphing these equations, I'm mainly looking for a way to know how to use that 'stretch/compress' factor to find additional points on the graph.  Thank you for your help. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #52281 by </B><A HREF=/tutors/aboutme.mpl?userid=stanbon><B>stanbon(75887)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=stanbon><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=52281\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Let's say you start with the graph of a parabola: y=x^2<BR>\n" );
document.write( "This is a statement regarding \"y\"; it is always \"the square of x\".<BR>\n" );
document.write( "Now, look at y=3x^2<BR>\n" );
document.write( "All those y-values are multiplied by 3; this \"stretches\" the curve so<BR>\n" );
document.write( "it goes upward faster: the parabola will look narrower because it rises so fast.<BR>\n" );
document.write( "Now look at y=(1/2)x^2<BR>\n" );
document.write( "All those original y-values are multiplid by (1/2); this \"compresses\" the<BR>\n" );
document.write( "curve so it looks flatter.<BR>\n" );
document.write( "---------<BR>\n" );
document.write( "There is no horizontal stretching or compressing but there is \"shifting\".<BR>\n" );
document.write( "If you start with y=x^2 the vertex will occur at x=0<BR>\n" );
document.write( "Replace \"x\" by \"x+3\" and the vertex will occur earlier on the x-axis; it will shift three to the left.<BR>\n" );
document.write( "Replace \"x\" by \"x-3\" and the vertex will occur later on the x-axis; it will <BR>\n" );
document.write( "shift three to the right.<BR>\n" );
document.write( "----------<BR>\n" );
document.write( "These are powerful tools for sketching curves.  Learn how to use them and <BR>\n" );
document.write( "you will save a lot of time you might otherwise use plotting points.\r<BR>\n" );
document.write( "\n" );
document.write( "Cheers,<BR>\n" );
document.write( "Stan H.   </SPAN>\n" );
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