document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=526102>Question 526102</A>: <I><SPAN STYLE=\"word-break: break-all;\"> how do i solve this problem idk where to begin or how to do it?<BR>\n" );
document.write( "Find an equation of a parabola that contains the points (1,4)(2,7) and (4,25) </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #348330 by </B><A HREF=/tutors/aboutme.mpl?userid=lwsshak3><B>lwsshak3(11628)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=lwsshak3><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=348330\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> how do i solve this problem idk where to begin or how to do it?<BR>\n" );
document.write( "Find an equation of a parabola that contains the points (1,4)(2,7) and (4,25)<BR>\n" );
document.write( "**<BR>\n" );
document.write( "Standard equation for a parabola: y=A(x-h)^2+k<BR>\n" );
document.write( "There are 3 variables you must solve: A, h, and k, and you have 3 known points on the curve.<BR>\n" );
document.write( "The approach, then, is to set up 3 equations with the 3 known points.<BR>\n" );
document.write( "..<BR>\n" );
document.write( "(1) 4=A(1-h)^2+k<BR>\n" );
document.write( "(2) 7=A(2-h)^2+k<BR>\n" );
document.write( "(3) 25=A(4-h)^2+k<BR>\n" );
document.write( "..<BR>\n" );
document.write( "(1) 4=A(1-h)^2+k<BR>\n" );
document.write( "4=A(1-2h+h^2)+k<BR>\n" );
document.write( "(4) 4=A-2Ah+Ah^2+k<BR>\n" );
document.write( "..<BR>\n" );
document.write( "(2) 7=A(2-h)^2+k<BR>\n" );
document.write( "7=A(4-4h+h^2)+k<BR>\n" );
document.write( "(5) 7=4A-4Ah+Ah^2+k<BR>\n" );
document.write( "..<BR>\n" );
document.write( "(4) 4=A-2Ah+Ah^2+k<BR>\n" );
document.write( "(5) 7=4A-4Ah+Ah^2+k<BR>\n" );
document.write( "subtract eq (5) fm eq(4)<BR>\n" );
document.write( "(6) -3=-3A+2Ah<BR>\n" );
document.write( "..<BR>\n" );
document.write( "(3) 25=A(4-h)^2+k<BR>\n" );
document.write( "25=A(16-8h+h^2)+k<BR>\n" );
document.write( "(7) 25=16A-8Ah+Ah^2+k<BR>\n" );
document.write( "(5) 7=4A-4Ah+Ah^2+k<BR>\n" );
document.write( "subtract eq (5) fm eq(7)<BR>\n" );
document.write( "(7) 18=12A-4Ah<BR>\n" );
document.write( "(6) -3=-3A+2Ah<BR>\n" );
document.write( "multiply eq(6) by 2<BR>\n" );
document.write( "(8) -6=-6A+4Ah<BR>\n" );
document.write( "Add eq(8) and eq(7)<BR>\n" );
document.write( "(9) 12=6A<BR>\n" );
document.write( "A=2<BR>\n" );
document.write( "(6) -3=-3A+2Ah<BR>\n" );
document.write( "-3=-6+4h<BR>\n" );
document.write( "4h=3<BR>\n" );
document.write( "h=3/4<BR>\n" );
document.write( "(4) 4=A-2Ah+Ah^2+k<BR>\n" );
document.write( "4=2-3+1.125+k<BR>\n" );
document.write( "k=3.875<BR>\n" );
document.write( "..<BR>\n" );
document.write( "Ans:<BR>\n" );
document.write( "A=2, h=.75, k=3.875<BR>\n" );
document.write( "Equation of parabola:<BR>\n" );
document.write( "y=2(x-.75)^2+3.875<BR>\n" );
document.write( "see graph below as a visual check on the answers:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+graph%28+300%2C+300%2C+-5%2C+5%2C+-10%2C+10%2C2%28x-.75%29%5E2%2B3.875%29+ ALIGN=MIDDLE  ALT=\"+graph%28+300%2C+300%2C+-5%2C+5%2C+-10%2C+10%2C2%28x-.75%29%5E2%2B3.875%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "..<BR>\n" );
document.write( "comment: This is quite a marathon. Hope you can follow it ok. The answers I got check with my computer graphing program. </SPAN>\n" );
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