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You can put this solution on YOUR website!
Given:
\n" ); document.write( "(1) y = a*x^2 + bx + c
\n" ); document.write( "Find (a,b,c) given
\n" ); document.write( "three points on the parabola
\n" ); document.write( "(a) (0,5)
\n" ); document.write( "(b) (2,-3) and
\n" ); document.write( "(c) (-1,12)
\n" ); document.write( "First substitute point (a) into (1) and get
\n" ); document.write( "(2) 5 = a*0 + b*0 + c or
\n" ); document.write( "(3) 5 = 0 + 0 + c or
\n" ); document.write( "(4) c = 5
\n" ); document.write( "Now put (b) and c into (1) and get
\n" ); document.write( "(5) -3 = 4a + 2b + 5 or
\n" ); document.write( "(6) 4a + 2b = -8
\n" ); document.write( "Now put (c) and c into (1) and get
\n" ); document.write( "(7) 12 = a - b + 5 or
\n" ); document.write( "(8) a - b = 7
\n" ); document.write( "Now solve (6) and (8) simultaneously to get a and b as follows;
\n" ); document.write( "First add twice (8) to (6) to get
\n" ); document.write( "(9) 6a + 0 = 6 or
\n" ); document.write( "(10) a = 1
\n" ); document.write( "Now put a into (8) to get
\n" ); document.write( "(11) 1 - b = 7 or
\n" ); document.write( "(12) b = -6
\n" ); document.write( "Let's check these value using point (c)
\n" ); document.write( "Is (12 = 1*(-1)^2 -6*(-1) + 5)?
\n" ); document.write( "Is (12 = 1 +6 +5)?
\n" ); document.write( "Is (12 = 12)? Yes
\n" ); document.write( "Answer: The parabola is y = x^2 -6x +5.\r
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