document.write( "Question 702058: A parabola has points at (-3,4) (1,10) and (3,8)\r
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document.write( "What is the standard form for this parabolic path? \n" );
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Algebra.Com's Answer #432868 by lwsshak3(11628)![]() ![]() ![]() You can put this solution on YOUR website! A parabola has points at (-3,4) (1,10) and (3,8) \n" ); document.write( "What is the standard form for this parabolic path? \n" ); document.write( "** \n" ); document.write( "Standard form of equation for a parabola: y=A(x-h)^2+k, (h,k)=(x,y) coordinates of the vertex. \n" ); document.write( "Set up 3 equations:y= Ax^2+Bx+c \n" ); document.write( "(-3,4) 4=9A-3B+c \n" ); document.write( "(1,10) 10=A+B+c \n" ); document.write( "(3,8) 8=9A+3B+c \n" ); document.write( ".. \n" ); document.write( "4=9A-3B+c \n" ); document.write( "10=A+B+c \n" ); document.write( "subtract \n" ); document.write( "-6=8A-4B \n" ); document.write( ".. \n" ); document.write( "4=9A-3B+c \n" ); document.write( "8=9A+3B+c \n" ); document.write( "subtract \n" ); document.write( "-4=-6B \n" ); document.write( "B=2/3 \n" ); document.write( ".. \n" ); document.write( "8A=4B-6=8/3-6 \n" ); document.write( "A=1/3-6/8=1/3-3/4=4/12-9/12=-5/12 \n" ); document.write( ".. \n" ); document.write( "c=10-A-B=10-(-5/12)-2/3=10+5/12-8/12=10-3/12=120/12-3/12=117/12 \n" ); document.write( ".. \n" ); document.write( "A=-5/12 \n" ); document.write( "B=2/3 \n" ); document.write( "c=117/12 \n" ); document.write( ".. \n" ); document.write( "y=Ax^2+Bx+c \n" ); document.write( "y=(-5/12)x^2+(2/3)x+117/12 \n" ); document.write( "complete the square: \n" ); document.write( "y=(-5/12)(x^2-(8/5)x+(64/100)+.8/3+117/12 \n" ); document.write( "y=(-5/12)(x-0.8)^2+10.016667 \n" ); document.write( "sorry, this problem has cumbersome numbers to work with \n" ); document.write( " \n" ); document.write( " |