document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=40036>Question 40036</A>: <I><SPAN STYLE=\"word-break: break-all;\"> for quadratic functions, sketch two parabolas showing all procedure (concavity, y-intercept, x-intercept, symmetric axis and vertex point)<BR>\n" );
document.write( "a. y=2x^2-3x+1<BR>\n" );
document.write( "b.y=-3x^2+2x+1 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #25471 by </B><A HREF=/tutors/aboutme.mpl?userid=venugopalramana><B>venugopalramana(3286)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=venugopalramana><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.geocities.com/venugopalramana/FREE_MATHS_ASSISTANCE.html valign=middle><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=25471\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\">  For quadratic functions, sketch two parabolas showing<BR>\n" );
document.write( "> all procedure(concavity, y-intercept, x-intercepts,<BR>\n" );
document.write( "> symmetric axis, and vertex point)<BR>\n" );
document.write( "> y=2x^2-3x+1...make x coefficient 1 and .complete square<BR>\n" );
document.write( "y=2{x^2-2*x*0.75+0.75^2}+1-2*0.75^2<BR>\n" );
document.write( "=2(x-0.75)^2-0.125...so this will have a minimum at x=0.75...then y =-0.125...so<BR>\n" );
document.write( "1.vertex is(0.75,-0.125)...it is a minimum...so parabola has a trough<BR>\n" );
document.write( "at the bottom or convex down wards .....concave upwards.<BR>\n" );
document.write( "2.axis of symmetry is x-0.75=0....or x=0.75<BR>\n" );
document.write( "3.when x =0....y=2*0.75^2-0.125=1...hence y intercept=1<BR>\n" );
document.write( "4.when y=0....2(x-0.75)^2=0.125......so x is<BR>\n" );
document.write( "REAL...that is it has 2 x interceptS..that is it  cutS x<BR>\n" );
document.write( "axis AT 2 PLACES<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+graph%28+600%2C+600%2C+-5%2C+5%2C+-5%2C+10%2C+2%2Ax%5E2-3%2Ax%2B1%29+ ALIGN=MIDDLE  ALT=\"+graph%28+600%2C+600%2C+-5%2C+5%2C+-5%2C+10%2C+2%2Ax%5E2-3%2Ax%2B1%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "5.as far as sketching goes , you can try that by<BR>\n" );
document.write( "1.draw x & y axes with a suitable scale.<BR>\n" );
document.write( "2.plot vertex at (0.75,1.125)<BR>\n" );
document.write( "3.draw axis of symmetry a vertical line at x=0.75<BR>\n" );
document.write( "4.plot th y intercept at x=0 and y=2.25..that is curve cuts y axis at 2.25<BR>\n" );
document.write( "5.sketch a symmetric graph from vertex upwards around the axis of<BR>\n" );
document.write( "symmetry of x=0.75\r<BR>\n" );
document.write( "\n" );
document.write( "> y=-3x^2+2x+1...same way as abov<BR>\n" );
document.write( "y=-3{x^2-2*x*(1/3)+(1/3)^2}+1+(1/3)^2<BR>\n" );
document.write( "=(10/9)-3{x-(1/3)}^2<BR>\n" );
document.write( "so....<BR>\n" );
document.write( "1.vertex is(1/3,10/9)...it is a maximum...so parabola has a peak at<BR>\n" );
document.write( "the top or convex up wards .....concave downwards.<BR>\n" );
document.write( "2.axis of symmetry is x-1/3=0....or x=1/3<BR>\n" );
document.write( "3.when x =0....y=10/9-3/9=7/9...hence y intercept=7/9<BR>\n" );
document.write( "4.when y=0....3{x-(1/3)}^2=10/9........so x is real=(1/3)+ and -<BR>\n" );
document.write( "sqrt(10/27)...that is it has 2.. x intercepts..that is it  cuts x axis<BR>\n" );
document.write( "at 2 places<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+graph%28+600%2C+600%2C+-5%2C+5%2C+-10%2C+5%2C+-3%2Ax%5E2%2B2%2Ax%2B1%29+ ALIGN=MIDDLE  ALT=\"+graph%28+600%2C+600%2C+-5%2C+5%2C+-10%2C+5%2C+-3%2Ax%5E2%2B2%2Ax%2B1%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "5.as far as sketching goes ,but you can try that by the same way as given above. </SPAN>\n" );
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