document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1203773>Question 1203773</A>: <I><SPAN STYLE=\"word-break: break-all;\"> f(x) = x^2 + 5\r<BR>\n" );
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document.write( "a) f(-6) =\r<BR>\n" );
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document.write( "b) Find if f(x) = 14\r<BR>\n" );
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document.write( "c) f(x + h) =\r<BR>\n" );
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document.write( "d) Calculate: f(x + h) - f(x) over h\r<BR>\n" );
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document.write( "Can you please explain to me this homework question by showing the step-by-step calculations? Thank you!  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #839604 by </B><A HREF=/tutors/aboutme.mpl?userid=mananth><B>mananth(16946)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=mananth><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=mananth><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=839604\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> \r<BR>\n" );
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document.write( "a)  find f(-6), plug -6 into the function \r<BR>\n" );
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document.write( "f(-6) = (-6)^2 + 5<BR>\n" );
document.write( "f(-6) = 36 + 5<BR>\n" );
document.write( "f(-6) = 41\r<BR>\n" );
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document.write( "b)  f(x) = 14,  find  x:\r<BR>\n" );
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document.write( "14 = x^2 + 5\r<BR>\n" );
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document.write( "Subtract 5 from both sides:\r<BR>\n" );
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document.write( "x^2 = 14 - 5<BR>\n" );
document.write( "x^2 = 9\r<BR>\n" );
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document.write( " take the square root of both sides:\r<BR>\n" );
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document.write( "x = ±sqrt(9)<BR>\n" );
document.write( "x = ±3\r<BR>\n" );
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document.write( "So,  x = 3 and x = -3.\r<BR>\n" );
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document.write( "c) To find f(x + h), you plug x + h  for x:\r<BR>\n" );
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document.write( "f(x + h) = (x + h)^2 + 5\r<BR>\n" );
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document.write( "d)  We know f(x+h) and f(x) from above\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28%28f%28x+%2B+h%29+-+f%28x%29%29%29%2Fh+ ALIGN=MIDDLE  ALT=\"%28%28f%28x+%2B+h%29+-+f%28x%29%29%29%2Fh+\"   DISABLED_style= \"max-width:90%; height:auto;\" >= <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28%28x+%2B+h%29%5E2+%2B+5+-+%28x%5E2+%2B+5%29%29%2Fh ALIGN=MIDDLE  ALT=\"%28%28x+%2B+h%29%5E2+%2B+5+-+%28x%5E2+%2B+5%29%29%2Fh\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( " simplify the  R H S\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x+%2B+h%29%5E2+%2B+5+-+%28x%5E2+%2B+5%29%2Fh ALIGN=MIDDLE  ALT=\"%28x+%2B+h%29%5E2+%2B+5+-+%28x%5E2+%2B+5%29%2Fh\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( " = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28%28x%5E2+%2B+2xh+%2B+h%5E2+%2B+5%29+-+%28x%5E2+%2B+5%29%29%2Fh ALIGN=MIDDLE  ALT=\"%28%28x%5E2+%2B+2xh+%2B+h%5E2+%2B+5%29+-+%28x%5E2+%2B+5%29%29%2Fh\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( " cancel x^2 and -x^2 we get\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%282xh+%2B+h%5E2%29%2Fh ALIGN=MIDDLE  ALT=\"%282xh+%2B+h%5E2%29%2Fh\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "h(2x + h)/h\r<BR>\n" );
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document.write( "So,<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+%28f%28x+%2B+h%29+-+f%28x%29%29%2Fh+=+2x+%2B+h. ALIGN=MIDDLE  ALT=\"+%28f%28x+%2B+h%29+-+f%28x%29%29%2Fh+=+2x+%2B+h.\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( " </SPAN>\n" );
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