document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1148201>Question 1148201</A>: <I><SPAN STYLE=\"word-break: break-all;\"> How do i make a quadratic equation from vertex point (4,-3) and point (6,-1)? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #769595 by </B><A HREF=/tutors/aboutme.mpl?userid=greenestamps><B>greenestamps(13200)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=greenestamps><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=greenestamps><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=769595\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <br><BR>\n" );
document.write( "Start with the vertex form of the equation, as tutor @MathTherapy did:<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+a%28x-h%29%5E2%2Bk ALIGN=MIDDLE  ALT=\"y+=+a%28x-h%29%5E2%2Bk\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "With the vertex given as (4,-3), the equation in this form is<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+a%28x-4%29%5E2-3 ALIGN=MIDDLE  ALT=\"y+=+a%28x-4%29%5E2-3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "Then here is an alternative method for determining the value of a to complete the equation.<br><BR>\n" );
document.write( "(1) The point other than the vertex that is given is 2 units to the right of the vertex.<BR>\n" );
document.write( "(2) If a were 1, so that the graph behaved like y=x^2, then the y value 2 to the right of the vertex would be 2^2=4 greater than the y value at the vertex.<BR>\n" );
document.write( "(3) But the y value 2 to the right of the vertex is only 2 greater than the y value at the vertex.<br><BR>\n" );
document.write( "Since the y value increased only half as much as it would have increased if a were 1, a must be 1/2.<br><BR>\n" );
document.write( "So the equation is<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+%281%2F2%29%28x-4%29%5E2-3 ALIGN=MIDDLE  ALT=\"y+=+%281%2F2%29%28x-4%29%5E2-3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );