document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=252705>Question 252705</A>: <I><SPAN STYLE=\"word-break: break-all;\"> determine the vertex of quadratic function stating axis of symmetry,minimum or maximum value,and domain and range on y=10x^2+5x-1<BR>\n" );
document.write( "and y=-24x^2+18x+11<BR>\n" );
document.write( "I am not understanding even though i read over examples. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #184759 by </B><A HREF=/tutors/aboutme.mpl?userid=drk><B>drk(1908)</B></A><img src=\"/images/stars/stars-12.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=drk><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=184759\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> let's start with the first equation and  then move to the second:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=10x%5E2%2B5x-1 ALIGN=MIDDLE  ALT=\"y=10x%5E2%2B5x-1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "quadratics are expressed as Y = Ax^2 + Bx + C.<BR>\n" );
document.write( "--<BR>\n" );
document.write( "vertex: <BR>\n" );
document.write( "We can find the vertex using -b/2a. -5/2*10 = -5/20 = -1/4. This is the x part of the vertex and now we put that into f(x) to get <BR>\n" );
document.write( "10(1/4)^2 + 5(1/4)-1 = 10/16 + 5/4 - 1 = 14/16 = 7/8.<BR>\n" );
document.write( "vertex = (1/4,7/8)<BR>\n" );
document.write( "--<BR>\n" );
document.write( "axis of symmetry:<BR>\n" );
document.write( "This is just the x value of the vertex<BR>\n" );
document.write( "x = 1/4.<BR>\n" );
document.write( "--<BR>\n" );
document.write( "min:<BR>\n" );
document.write( "since the graph opens up, there will be a min at the vertex.<BR>\n" );
document.write( "min @ (1/4,7/8)<BR>\n" );
document.write( "--<BR>\n" );
document.write( "domain:domain: For a parabola opening up or down, domain will be all reals.<BR>\n" );
document.write( "range: Since the parabola opens up, the minimum range is 7/8. So we have Y >= 7/8.\r<BR>\n" );
document.write( "\n" );
document.write( "-- EQUATION #2<BR>\n" );
document.write( "{{y = -24x^2 + 18x + 11}}<BR>\n" );
document.write( "quadratics are expressed as Y = Ax^2 + Bx + C.<BR>\n" );
document.write( "--<BR>\n" );
document.write( "vertex: <BR>\n" );
document.write( "We can find the vertex using -b/2a. -18/2*-24 = 18/48 = 3/8. This is the x part of the vertex and now we put that into f(x) to get <BR>\n" );
document.write( "-24(3/8)^2 + 18(3/8) + 11 = -27/8 + 27/4 + 11 = 115/4.<BR>\n" );
document.write( "vertex = (3/8, 115/4)<BR>\n" );
document.write( "--<BR>\n" );
document.write( "axis of symmetry:<BR>\n" );
document.write( "This is just the x value of the vertex<BR>\n" );
document.write( "x = 3/8.<BR>\n" );
document.write( "--<BR>\n" );
document.write( "min: No min in this case.\r<BR>\n" );
document.write( "\n" );
document.write( "max: SInce the graph opens down, there will be a max at the vertex.<BR>\n" );
document.write( "min @ (3/8, 115/4)<BR>\n" );
document.write( "--<BR>\n" );
document.write( "domain: For a parabola opening up or down, domain will be all reals.<BR>\n" );
document.write( "range: Since the parabola opens down, the highest range is 115/4. So we have Y <= 115/4. </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );