document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=128294>Question 128294</A>: <I><SPAN STYLE=\"word-break: break-all;\"> At an airshow, a plane is in a power dive. The height of the plane, in metres above the ground , is recorded for the first six seconds.<BR>\n" );
document.write( "Time(s): 1,2,3,4,5,6<BR>\n" );
document.write( "Height(m): 214,180,150,124,102,84<BR>\n" );
document.write( "a) Algebraically determine the quadratic function that models the path followed by the plane. Express the function in the form y=ax^2+bx+c.<BR>\n" );
document.write( "b) Use the function to determine the minimum height of the plane. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #93928 by </B><A HREF=/tutors/aboutme.mpl?userid=stanbon><B>stanbon(75887)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=stanbon><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=93928\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> At an airshow, a plane is in a power dive. The height of the plane, in metres above the ground , is recorded for the first six seconds.<BR>\n" );
document.write( "Time(s): 1,2,3,4,5,6<BR>\n" );
document.write( "Height(m): 214,180,150,124,102,84<BR>\n" );
document.write( "a) Algebraically determine the quadratic function that models the path followed by the plane. Express the function in the form y=ax^2+bx+c.<BR>\n" );
document.write( "--------<BR>\n" );
document.write( "Substitute three x/y pairs into the form to get three equations <BR>\n" );
document.write( "with variables a,b, and c.<BR>\n" );
document.write( "-------------------------------<BR>\n" );
document.write( "f(1) = a  +  b  +  c = 214<BR>\n" );
document.write( "f(2) =4a  + 2b  +  c = 180<BR>\n" );
document.write( "f(3) =9a  + 3b  +  c = 150<BR>\n" );
document.write( "----------------------------<BR>\n" );
document.write( "I used the Matrix function of a TI calculator to find the following:<BR>\n" );
document.write( "a = 2<BR>\n" );
document.write( "b = -40<BR>\n" );
document.write( "c = 252<BR>\n" );
document.write( "------------<BR>\n" );
document.write( "EQUATION:<BR>\n" );
document.write( "y = 2x^2-40x+252<BR>\n" );
document.write( "-------------------\r<BR>\n" );
document.write( "\n" );
document.write( "b) Use the function to determine the minimum height of the plane.<BR>\n" );
document.write( "minimum occurs at x = -b/2a = 40/4 = 10<BR>\n" );
document.write( "f(10) = 52<BR>\n" );
document.write( "-----------------<BR>\n" );
document.write( "At 10 seconds the plane will be at 52 ft.<BR>\n" );
document.write( "=======================<BR>\n" );
document.write( "Cheers,<BR>\n" );
document.write( "Stan H.<BR>\n" );
document.write( "---------------------- </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );