document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=478190>Question 478190</A>: <I><SPAN STYLE=\"word-break: break-all;\"> what is the vertex of f(x)=x^2-8x-5<BR>\n" );
document.write( "                      f(x)=-x^2+10x+6<BR>\n" );
document.write( "                      f(x)=3x^2-12x+9<BR>\n" );
document.write( "                      f(x)=-2x^2+2x+7<BR>\n" );
document.write( "                      f(x)=8-x^2\r<BR>\n" );
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document.write( "I have bee trying to solve and find the vertexes for these five problems since last Sunday. I don't understand quadratic equations at all. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #327668 by </B><A HREF=/tutors/aboutme.mpl?userid=htmentor><B>htmentor(1343)</B></A><img src=\"/images/stars/stars-12.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=htmentor><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=htmentor><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=327668\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The vertex of a quadratic function is the turning point of the function. <BR>\n" );
document.write( "At this point, the slope of the function, dy/dx = 0.  <BR>\n" );
document.write( "The equation for the function in standard form is:<BR>\n" );
document.write( "y = ax^2 + bx + c<BR>\n" );
document.write( "To find the vertex, compute dy/dx and set equal to 0:<BR>\n" );
document.write( "dy/dx = 0 = 2ax + b<BR>\n" );
document.write( "Solving for x gives x = -b/2a<BR>\n" );
document.write( "Now substitute this value back in the original equation to get the y-value of the vertex:<BR>\n" );
document.write( "y = a(-b/2a)^2 + b(-b/2a) + c<BR>\n" );
document.write( "This gives y = c - b^2/(4a)<BR>\n" );
document.write( "We can use this information to find the vertices of the given functions.<BR>\n" );
document.write( "e.g. f(x) = x^2-8x-5<BR>\n" );
document.write( "The vertex is x = 8/2 = 4; y = -5 - (-8^2/4) -> y = -21<BR>\n" );
document.write( "I will leave it to you to compute the rest!<BR>\n" );
document.write( "Ans: (4,-21)<BR>\n" );
document.write( "We can graph the function to check our answer<BR>\n" );
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