document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=428848>Question 428848</A>: <I><SPAN STYLE=\"word-break: break-all;\"> How can I find the vertex while using the quadratic formula?<BR>\n" );
document.write( "y= -5x^+25x+70  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #298088 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=298088\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Set y=0 to find the points where the graph crosses the x-axis:<BR>\n" );
document.write( "-5x^2 + 25x + 70 = 0<BR>\n" );
document.write( "We can simplify by dividing through by -5:<BR>\n" );
document.write( "x^2 - 5x - 14 = 0<BR>\n" );
document.write( "x = (5 +- sqrt(25 + 56))/2 -> (5 +- 9)/2, or x = -2,7<BR>\n" );
document.write( "The vertex lies on the line of symmetry half way between these 2 points:<BR>\n" );
document.write( "x = (-2+7)/2, or x = 5/2<BR>\n" );
document.write( "To get the y-coordinate, substitute into original equation:<BR>\n" );
document.write( "-5*(5/2)^2 + 25(5/2) + 70 = -125/4 + 125/2 + 70 = 125/4 + 280/4 = 101 1/4<BR>\n" );
document.write( "Ans: vertex = (2 1/2,101 1/4)<BR>\n" );
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document.write( "</TD></TR></TABLE>\n" );