document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=175333>Question 175333</A>: <I><SPAN STYLE=\"word-break: break-all;\"> make a quadratic equation with the maximum value 10 and the x intercepts 1 and 3 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #130606 by </B><A HREF=/tutors/aboutme.mpl?userid=ankor@dixie-net.com><B>ankor@dixie-net.com(22740)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=ankor@dixie-net.com><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=ankor@dixie-net.com><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=130606\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> make a quadratic equation with the maximum value 10 and the x intercepts 1 and 3<BR>\n" );
document.write( ":<BR>\n" );
document.write( "we know that the max value of y is on the axis of symmetry which is half-way<BR>\n" );
document.write( "between the intercepts so max (vertex) is a x=2; y=10<BR>\n" );
document.write( ";<BR>\n" );
document.write( "we have three coordinates of this equation:<BR>\n" );
document.write( "x=1, y=0<BR>\n" );
document.write( "x=2, y=10<BR>\n" );
document.write( "x=3, y=0<BR>\n" );
document.write( ":<BR>\n" );
document.write( "Using the form ax^2 + bx + c = y, we can solve for a, b, c<BR>\n" );
document.write( ";<BR>\n" );
document.write( "x=1,y=0<BR>\n" );
document.write( "eq1: a + b + c = 0<BR>\n" );
document.write( ":<BR>\n" );
document.write( "x=2,y=10<BR>\n" );
document.write( "eq2: 4a + 2b + c = 10<BR>\n" );
document.write( ":<BR>\n" );
document.write( "x=3,y=0<BR>\n" );
document.write( "eq3: 9a + 3b + c = 0<BR>\n" );
document.write( ":<BR>\n" );
document.write( "Using equations 2 and 1, eliminate c<BR>\n" );
document.write( "4a + 2b + c = 10<BR>\n" );
document.write( " a +  b + c = 0<BR>\n" );
document.write( "-------------------subtraction eliminates c<BR>\n" );
document.write( "3a + b = 10<BR>\n" );
document.write( ":<BR>\n" );
document.write( "Using equations 2 and 3, eliminate c again<BR>\n" );
document.write( "4a + 2b + c = 10<BR>\n" );
document.write( "9a + 3b = c = 0<BR>\n" );
document.write( "---------------------subtract<BR>\n" );
document.write( "-5a - b = 10<BR>\n" );
document.write( ":<BR>\n" );
document.write( "Add these two a&b equations<BR>\n" );
document.write( "3a + b = 10<BR>\n" );
document.write( "-5a- b = 10<BR>\n" );
document.write( "----------------additions eliminates b<BR>\n" );
document.write( "-2a = 20<BR>\n" );
document.write( "a = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=20%2F%28-2%29 ALIGN=MIDDLE  ALT=\"20%2F%28-2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "a = -10<BR>\n" );
document.write( ":<BR>\n" );
document.write( "Find b using equation 3a + b = 10, substitute -10 for a<BR>\n" );
document.write( "3(-10) + b = 10<BR>\n" );
document.write( "-30 + b = 10<BR>\n" );
document.write( "b = 40<BR>\n" );
document.write( ":<BR>\n" );
document.write( "Find c using eq1:<BR>\n" );
document.write( "-10 + 40 + c = 0<BR>\n" );
document.write( "30 + c = 0<BR>\n" );
document.write( "c = -30<BR>\n" );
document.write( ":<BR>\n" );
document.write( "Our equation: y = -10x^2 + 40x - 30<BR>\n" );
document.write( ";<BR>\n" );
document.write( "Looks like this:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+graph%28+300%2C+200%2C+-3%2C+5%2C+-6%2C+12%2C+-10x%5E2%2B40x-30%29+ ALIGN=MIDDLE  ALT=\"+graph%28+300%2C+200%2C+-3%2C+5%2C+-6%2C+12%2C+-10x%5E2%2B40x-30%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );