document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1209637>Question 1209637</A>: <I><SPAN STYLE=\"word-break: break-all;\"> For parts (a) through (d), let f(x) = 2x^2 - 13x + 20 - 5x^2 + 19x + 7.\r<BR>\n" );
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document.write( "What is the vertex of the parabola y = f(x)?\r<BR>\n" );
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document.write( "Enter your answer as a coordinate pair, that is, as $(x,y)$ where $x$ and $y$ are replaced by numbers. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #849728 by </B><A HREF=/tutors/aboutme.mpl?userid=CPhill><B>CPhill(1959)</B></A><img src=\"/images/stars/stars-12.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=CPhill><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=CPhill><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=849728\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Here's how to find the vertex of the parabola:\r<BR>\n" );
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document.write( "1. **Simplify the function:**\r<BR>\n" );
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document.write( "Combine like terms in the given function:\r<BR>\n" );
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document.write( "f(x) = (2x² - 5x²) + (-13x + 19x) + (20 + 7)<BR>\n" );
document.write( "f(x) = -3x² + 6x + 27\r<BR>\n" );
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document.write( "2. **Find the x-coordinate of the vertex:**\r<BR>\n" );
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document.write( "The x-coordinate of the vertex of a parabola in the form ax² + bx + c is given by:\r<BR>\n" );
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document.write( "x = -b / 2a\r<BR>\n" );
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document.write( "In our simplified equation, a = -3 and b = 6.  So:\r<BR>\n" );
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document.write( "x = -6 / (2 * -3)<BR>\n" );
document.write( "x = -6 / -6<BR>\n" );
document.write( "x = 1\r<BR>\n" );
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document.write( "3. **Find the y-coordinate of the vertex:**\r<BR>\n" );
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document.write( "Substitute the x-coordinate (x = 1) back into the simplified function to find the y-coordinate:\r<BR>\n" );
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document.write( "f(1) = -3(1)² + 6(1) + 27<BR>\n" );
document.write( "f(1) = -3 + 6 + 27<BR>\n" );
document.write( "f(1) = 30\r<BR>\n" );
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document.write( "4. **Vertex coordinates:**\r<BR>\n" );
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document.write( "The vertex of the parabola is (x, y) = (1, 30).\r<BR>\n" );
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document.write( "Therefore, the vertex of the parabola y = f(x) is $(1, 30)$.<BR>\n" );
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