document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=637209>Question 637209</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I was never taught parabolas in school, so if someone could explain them too me and how to solve these problems, it would be much appreicated.\r<BR>\n" );
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document.write( "A parabola with equation y = ax^2 + bx passes through the two points (-1,3) and (4,-2). \r<BR>\n" );
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document.write( "(a) Use algebra to find its equation. <BR>\n" );
document.write( "Hint: Set up a system of two simultaneous equations. \r<BR>\n" );
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document.write( "(b) Is the point (2,-3) on the parabola? Justify your answer with working. <BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #401512 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=401512\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> A parabola with equation y = ax^2 + bx passes through the two points (-1,3) and (4,-2). <BR>\n" );
document.write( "(a) Use algebra to find its equation. <BR>\n" );
document.write( "Hint: Set up a system of two simultaneous equations. <BR>\n" );
document.write( "(b) Is the point (2,-3) on the parabola? Justify your answer with working. <BR>\n" );
document.write( "**<BR>\n" );
document.write( "Graph of a parabola: y=ax^2+bx+c<BR>\n" );
document.write( "3 equations are needed to solve, not 2<BR>\n" );
document.write( "..<BR>\n" );
document.write( "(1)   3=a(-1)^2+b(-1)+c<BR>\n" );
document.write( "(2) -2=a(4)^2+b(4)+c<BR>\n" );
document.write( "(3) -3=a(2)^2+b(2)+c<BR>\n" );
document.write( "..<BR>\n" );
document.write( "(1)   3=a-b+c<BR>\n" );
document.write( "(2) -2=16a+4b+c<BR>\n" );
document.write( "(3) -3=4a+2b+c<BR>\n" );
document.write( "..<BR>\n" );
document.write( "(1)   3=a-b+c<BR>\n" );
document.write( "(2) -2=16a+4b+c<BR>\n" );
document.write( "subtract to eliminate c<BR>\n" );
document.write( "(4)  5=-15a-5b<BR>\n" );
document.write( "..<BR>\n" );
document.write( "(2) -2=16a+4b+c<BR>\n" );
document.write( "(3) -3=4a+2b+c<BR>\n" );
document.write( "subtract to eliminate c<BR>\n" );
document.write( "(5)  1=12a+2b<BR>\n" );
document.write( "..<BR>\n" );
document.write( "(4)  5=-15a-5b<BR>\n" );
document.write( "(5)  1=12a+2b<BR>\n" );
document.write( "..<BR>\n" );
document.write( "(6) 10=-30a-10b<BR>\n" );
document.write( "(7)   5=  60a+10b<BR>\n" );
document.write( "add to eliminate b<BR>\n" );
document.write( "(8) 15=30a<BR>\n" );
document.write( "a=15/30=1/2<BR>\n" );
document.write( "2b=1-12a=1-6=-5<BR>\n" );
document.write( "b=-5/2<BR>\n" );
document.write( "c=3-a+b=3-1/2-5/2=0<BR>\n" );
document.write( "..<BR>\n" );
document.write( "a=1/2<BR>\n" );
document.write( "b=-5/2<BR>\n" );
document.write( "c=0<BR>\n" );
document.write( "..<BR>\n" );
document.write( "equation: <BR>\n" );
document.write( "y=(1/2) x^2-(5/2)x+0<BR>\n" );
document.write( "y=x^2/2-5x/2<BR>\n" );
document.write( "..<BR>\n" );
document.write( "Since point (2,-3) was used in developing the equation, it is on the curve of the parabola.<BR>\n" );
document.write( "note: In developing the equation of a parabola the constant c must also be considered and you would need 3 variables and 3 simultaneous equations. In this case c turned out to be =0, but this is not aways the case.<BR>\n" );
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