document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=67835>Question 67835</A>: <I><SPAN STYLE=\"word-break: break-all;\"> 1. From a square piece of cardboard with wisth x inches, a square of width x-3 inches is removed from the center. Write the area of the remaining piece as a function of x.\r<BR>\n" );
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document.write( "2. If P(4, -5) is a point on the graph of the function y=f(x), find the corresponding point on the graph of y=2f(x-6).\r<BR>\n" );
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document.write( "3. Explain how the graph of y-5=(x-3)2 power can be obtained from the graph of y=x2.\r<BR>\n" );
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document.write( "4. Determine the vertex of y=x2-8x+22.<BR>\n" );
document.write( "5. Find the maximum value of y=-x2 + 6x.<BR>\n" );
document.write( "6. Given f(x)=5x+7 and g(x)=x2+7, find (g o f)(x). </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #48233 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=48233\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> 1. From a square piece of cardboard with wisth x inches, a square of width x-3 inches is removed from the center. Write the area of the remaining piece as a function of x.<BR>\n" );
document.write( "Remaining area = original area - area cut out<BR>\n" );
document.write( "A(x) = x^2 - (x-3)^2<BR>\n" );
document.write( "A(x) = x^2-[x^2-6x+9]<BR>\n" );
document.write( "A(x) = 6x-9<BR>\n" );
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document.write( "2. If P(4, -5) is a point on the graph of the function y=f(x), find the corresponding point on the graph of y=2f(x-6).<BR>\n" );
document.write( "(x-6) moves the point 6 to the right to (10,-5)<BR>\n" );
document.write( "2 doubles the y value so you end up at (10,-10)<BR>\n" );
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document.write( "3. Explain how the graph of y-5=(x-3)^2 power can be obtained from the graph of y=x^2. <BR>\n" );
document.write( "(x-3) moves the parabola 3 to the right.<BR>\n" );
document.write( "5 then moves the parabola 5 up.<BR>\n" );
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document.write( "4. Determine the vertex of y=x^2-8x+22.<BR>\n" );
document.write( "The x-value is at -b/2a = 8/2=4<BR>\n" );
document.write( "Then f(4)=16-32+22 = 6<BR>\n" );
document.write( "Vertex at (4,6)<BR>\n" );
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document.write( "5. Find the maximum value of y=-x^2 + 6x.<BR>\n" );
document.write( "max occurs at the vertex where x=-b/2a = -6/-2=3<BR>\n" );
document.write( "f(3)=-9+18=9<BR>\n" );
document.write( "Max at (3,9)<BR>\n" );
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document.write( "6. Given f(x)=5x+7 and g(x)=x^2+7, find (g o f)(x).<BR>\n" );
document.write( "g[5x+7]=(5x+7)^2+7 = 25x^2+70x+56<BR>\n" );
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document.write( "Cheers,<BR>\n" );
document.write( "Stan H.<BR>\n" );
document.write( " </SPAN>\n" );
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