document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=144378>Question 144378</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Hi, again thanks for all the help it is great during finals week.<BR>\n" );
document.write( "Find the vertex and intercepts then graph the equation state if the concave is up or down.<BR>\n" );
document.write( "f(x)=3(x-2)^2-3.<BR>\n" );
document.write( "Thanks. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #105122 by </B><A HREF=/tutors/aboutme.mpl?userid=nabla><B>nabla(475)</B></A><img src=\"/images/stars/stars-10.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=nabla><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=105122\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> f(x)=3(x-2)^2-3\r<BR>\n" );
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document.write( "Notice that (x-2)^2 is always going to be >=0. Thus, the absolute minimum (we know it is a minimum due to the reasoning supplied for concavity below) of this function will be where that expression is 0. Namely, f(2)=-3. By definition this will be the vertex. Now, the function must open upward because the x^2 term will be positive with a coefficient of 3 upon expansion. x^2 is the driving term in this function.\r<BR>\n" );
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document.write( "Since it opens upward, we will have upward concavity. \r<BR>\n" );
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document.write( "As for intercepts:\r<BR>\n" );
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document.write( "x-ints: 0=3(x-2)^2-3<BR>\n" );
document.write( "is the same as  0=(x-2)^2-1<BR>\n" );
document.write( "is the same as 0=x^2-4x+3<BR>\n" );
document.write( "is the same as 0=(x-3)(x-1)<BR>\n" );
document.write( "which implies x=3 or x=1.<BR>\n" );
document.write( "f(3)=0. This gives (3,0)<BR>\n" );
document.write( "f(1)=0. This gives (1,0).\r<BR>\n" );
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document.write( "y-int: y=3(0-2)^2-3=9. This gives (0,9).\r<BR>\n" );
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document.write( "I will graph this even though it's not asked for:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28+300%2C+200%2C+-10%2C+10%2C+-10%2C+10%2C+3%28x-2%29%5E2-3+%29 ALIGN=MIDDLE  ALT=\"graph%28+300%2C+200%2C+-10%2C+10%2C+-10%2C+10%2C+3%28x-2%29%5E2-3+%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
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