document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1195810>Question 1195810</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A toy rocket is fired off the ground at a target 20 feet away. It is designed to reach a<BR>\n" );
document.write( "maximum height of 40 feet as it heads toward its target on a parabolic path. Find the<BR>\n" );
document.write( "equation that represents the height off the ground versus the distance travelled for this<BR>\n" );
document.write( "rocket. State the equation in the form 𝑦 = 𝑎𝑥<BR>\n" );
document.write( "2 + 𝑏𝑥 + 𝑐. [HINT: The path of the rocket is<BR>\n" );
document.write( "an “upside down” parabola, with one of the x-intercepts at the origin and the other at<BR>\n" );
document.write( "(20,0). We also know the y-value of the vertex. We can use this information to find “a”,<BR>\n" );
document.write( "the coefficient of the x2<BR>\n" );
document.write( "term. One way to find this is to plug the known values into the<BR>\n" );
document.write( "factored form of the equation, ie. 𝑦 = 𝑎(𝑥 − 𝑟)(𝑥 − 𝑠)] </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #828352 by </B><A HREF=/tutors/aboutme.mpl?userid=Alan3354><B>Alan3354(69443)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Alan3354><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=Alan3354><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=828352\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> A toy rocket is fired off the ground at a target 20 feet away. It is designed to reach a maximum height of 40 feet as it heads toward its target on a parabolic path. Find the equation that represents the height off the ground versus the distance travelled for this rocket<BR>\n" );
document.write( "--------------<BR>\n" );
document.write( "Put the apogee above the Origin.<BR>\n" );
document.write( "3 points on the parabola are<BR>\n" );
document.write( "A(-10,0), B(0,40) and C(10,0)<BR>\n" );
document.write( "------------<BR>\n" );
document.write( "y = ax^2 + bx + c is a parabola<BR>\n" );
document.write( "---<BR>\n" );
document.write( "Point A:<BR>\n" );
document.write( "0 = a*(-10)^2 + b*-10 + c = 0<BR>\n" );
document.write( "100a - 10b + c = 0<BR>\n" );
document.write( "---<BR>\n" );
document.write( "Point B:<BR>\n" );
document.write( "a*0 + b*0 + c = 40 ---> c = 40<BR>\n" );
document.write( "---<BR>\n" );
document.write( "Point C:<BR>\n" );
document.write( "a*(10)^2 + b*10 + c = 0<BR>\n" );
document.write( "100a + 10b + c = 0<BR>\n" );
document.write( "100a - 10b + c = 0 --- Point A<BR>\n" );
document.write( "---------------------------------------- Subtract<BR>\n" );
document.write( "20b = 0<BR>\n" );
document.write( "b = 0<BR>\n" );
document.write( "=================<BR>\n" );
document.write( "100a - 10b + c = 0 --- Point A<BR>\n" );
document.write( "100a + c = 0<BR>\n" );
document.write( "100a + 40 = c<BR>\n" );
document.write( "a = -0.4<BR>\n" );
document.write( "=================<BR>\n" );
document.write( "y = -0.4x^2 + 40 is the equation WITH the center at the Origin.<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );