document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1042738>Question 1042738</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Determine, without graphing, whether the given quadratic function has a maximum value or a minimum value and then find that value.\r<BR>\n" );
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document.write( "f(x) = -x2 - 2x + 2<BR>\n" );
document.write( "    a. minimum; - 1<BR>\n" );
document.write( "    b. maximum; 3<BR>\n" );
document.write( "    c. minimum; 3<BR>\n" );
document.write( "    d. maximum; - 1 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #657779 by </B><A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><B>jim_thompson5910(35256)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><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=657779\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> f(x) = -x^2 - 2x + 2\r<BR>\n" );
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document.write( "-x^2 - 2x + 2 has the leading coefficient of -1. The negative leading coefficient means that the parabola opens downward.\r<BR>\n" );
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document.write( "The parabola opening downward is like an upside down bowl shape. So this function has a <font color=red>maximum</font>. Think of it as the peak of the mountain. \r<BR>\n" );
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document.write( "In the case of -x^2 - 2x + 2, the values of a,b,c are\r<BR>\n" );
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document.write( "a = -1<BR>\n" );
document.write( "b = -2<BR>\n" );
document.write( "c = 2\r<BR>\n" );
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document.write( "Plug a = -1 and b = -2 into x = -b/(2a) to get\r<BR>\n" );
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document.write( "x = -b/(2a)<BR>\n" );
document.write( "x = -(-2)/(2(-1))<BR>\n" );
document.write( "x = -(-2)/(-2)<BR>\n" );
document.write( "x = 2/(-2)<BR>\n" );
document.write( "x = -1\r<BR>\n" );
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document.write( "So the max y value occurs when x = -1. Plug x = -1 into the original function to find the corresponding value of y.\r<BR>\n" );
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document.write( "f(x) = -x^2 - 2x + 2<BR>\n" );
document.write( "f(-1) = -(-1)^2 - 2(-1) + 2<BR>\n" );
document.write( "f(-1) = -(1) - 2(-1) + 2<BR>\n" );
document.write( "f(-1) = -1 - 2(-1) + 2<BR>\n" );
document.write( "f(-1) = -1 +2 + 2<BR>\n" );
document.write( "f(-1) = 1 + 2<BR>\n" );
document.write( "f(-1) = 3\r<BR>\n" );
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document.write( "When x = -1, the corresponding y value is y = 3<BR>\n" );
document.write( "The two values pair up to get this point (-1,3)\r<BR>\n" );
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document.write( "The vertex is at the point (-1,3)\r<BR>\n" );
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document.write( "Therefore, the <font color=red>maximum</font> value is y = <font color=red>3</font> \r<BR>\n" );
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document.write( "So the answer must be  <font color=red>choice B</font> </SPAN>\n" );
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