document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=126975>Question 126975</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Hi I keep doing something wrong in this problem. Can you help me solve it? thanks\r<BR>\n" );
document.write( "\n" );
document.write( "A function is given below. Determine the average rate of change of the function between x = -4 and x = 1.\r<BR>\n" );
document.write( "\n" );
document.write( "h(t) = t^2 - 10t  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #92996 by </B><A HREF=/tutors/aboutme.mpl?userid=solver91311><B>solver91311(24713)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=solver91311><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=solver91311><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=92996\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The average rate of change of f(x) between x = a and x = b is given by the slope of the line that passes through the points (a, f(a)) and (b, f(b)) (called a secant line).  Given two points, you can calculate a slope using the formula:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=m=%28y%5B1%5D-y%5B2%5D%29%2F%28x%5B1%5D-x%5B2%5D%29 ALIGN=MIDDLE  ALT=\"m=%28y%5B1%5D-y%5B2%5D%29%2F%28x%5B1%5D-x%5B2%5D%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >, so for the slope of the described secant line:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28f%28a%29-f%28b%29%29%2F%28a-b%29 ALIGN=MIDDLE  ALT=\"%28f%28a%29-f%28b%29%29%2F%28a-b%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "For your function:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a+=+-4 ALIGN=MIDDLE  ALT=\"a+=+-4\"   DISABLED_style= \"max-width:90%; height:auto;\" >, so <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28a%29=f%28-4%29=%28-4%29%5E2-10%28-4%29=16%2B40=56 ALIGN=MIDDLE  ALT=\"f%28a%29=f%28-4%29=%28-4%29%5E2-10%28-4%29=16%2B40=56\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b=+1 ALIGN=MIDDLE  ALT=\"b=+1\"   DISABLED_style= \"max-width:90%; height:auto;\" >, so <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28b%29=f%281%29=%281%29%5E2-10%281%29=1-10=-9 ALIGN=MIDDLE  ALT=\"f%28b%29=f%281%29=%281%29%5E2-10%281%29=1-10=-9\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28f%28a%29-f%28b%29%29%2F%28a-b%29=%2856-%28-9%29%29%2F%28-4-1%29=65%2F-5=-13 ALIGN=MIDDLE  ALT=\"%28f%28a%29-f%28b%29%29%2F%28a-b%29=%2856-%28-9%29%29%2F%28-4-1%29=65%2F-5=-13\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Let's draw a picture and see if the answer makes sense:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=drawing%28600%2C600%2C-10%2C10%2C-60%2C60%2C%0D%0Agrid%281%29%2C%0D%0Agraph%28600%2C600%2C-10%2C10%2C-60%2C60%2Cx%5E2-10x%2C-13x%2B4%29%0D%0A%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "The secant line pictured doesn't look as steep as it should be for a -13 slope, but that is because I have different scales for the x and y axis so that you can actually see something.  But the intersection points look correct and the configuration of the parabola is right (vertex at (5,-25), zeros at 0 and 10, concave up, etc.) </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );