document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1198841>Question 1198841</A>: <I><SPAN STYLE=\"word-break: break-all;\"> 4. Describe the transformations applied to f(x)=x2 to produce the function 	 		f(x)=2(x-5)2+10\r<BR>\n" );
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document.write( "5. Convert the following equation into vertex form by completing the square.<BR>\n" );
document.write( "f(x) = 2x2+12x-4\r<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #832496 by </B><A HREF=/tutors/aboutme.mpl?userid=math_tutor2020><B>math_tutor2020(3817)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=math_tutor2020><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=832496\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font color=black size=3><BR>\n" );
document.write( "To represent an exponent using your keyboard, type the symbol ^\r<BR>\n" );
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document.write( "Example: <BR>\n" );
document.write( "x^2 means <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2 ALIGN=MIDDLE  ALT=\"x%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Problem 4\r<BR>\n" );
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document.write( "y = x^2  is the parent quadratic function<BR>\n" );
document.write( "y = 2x^2  vertically stretches the curve by a factor of 2<BR>\n" );
document.write( "y = 2(x-5)^2  shifts the curve 5 units to the right<BR>\n" );
document.write( "y = 2(x-5)^2+10  shifts the curve 10 unit up\r<BR>\n" );
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document.write( "Graph:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28500%2C500%2C-10%2C10%2C-5%2C15%2Cx%5E2%2C2x%5E2%2C2%28x-5%29%5E2%2C2%28x-5%29%5E2%2B10%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "x^2 in red<BR>\n" );
document.write( "2x^2 in green<BR>\n" );
document.write( "2(x-5)^2 in blue<BR>\n" );
document.write( "2(x-5)^2+10 in purple\r<BR>\n" );
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document.write( "Here's a graph of just the parent x^2 and the final result 2(x-5)^2+10<BR>\n" );
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document.write( "I recommend using either Desmos or GeoGebra as a graphing tool.<BR>\n" );
document.write( "Both of which are free.\r<BR>\n" );
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document.write( "Take notice how the vertex (0,0) in the parent function has been shifted 5 units right and 10 units up to arrive at (5,10) on the final result.\r<BR>\n" );
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document.write( "Problem 5\r<BR>\n" );
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document.write( "y = 2x^2+12x-4 is of the form y = ax^2+bx+c<BR>\n" );
document.write( "where,<BR>\n" );
document.write( "a = 2<BR>\n" );
document.write( "b = 12<BR>\n" );
document.write( "c = -4\r<BR>\n" );
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document.write( "Use the first two values to find the following<BR>\n" );
document.write( "h = -b/(2a)<BR>\n" );
document.write( "h = -12/(2*2)<BR>\n" );
document.write( "h = -3<BR>\n" );
document.write( "This is the x coordinate of the vertex (h,k)\r<BR>\n" );
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document.write( "Use that to find the y coordinate of the vertex.<BR>\n" );
document.write( "y = 2x^2+12x-4<BR>\n" );
document.write( "y = 2(-3)^2+12(-3)-4<BR>\n" );
document.write( "y = -22<BR>\n" );
document.write( "The k value is k = -22\r<BR>\n" );
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document.write( "The vertex is located at (h,k) = (-3,-22)\r<BR>\n" );
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document.write( "So,<BR>\n" );
document.write( "y = a(x-h)^2 + k<BR>\n" );
document.write( "y = 2(x-(-3))^2 + (-22)<BR>\n" );
document.write( "y = 2(x+3)^2 - 22<BR>\n" );
document.write( "represents the vertex form.\r<BR>\n" );
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document.write( "Graph:<BR>\n" );
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document.write( "As mentioned in the previous problem, use graphing software to confirm the answer.<BR>\n" );
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