document.write( "Question 424932: 16 = if x=1 then y=2;
\n" ); document.write( "if x=2 then y=4;
\n" ); document.write( "if x=3 then y=7;
\n" ); document.write( "if x=4 then y=11;
\n" ); document.write( "if x=5 then y=16;\r
\n" ); document.write( "\n" ); document.write( "What will be the formula to solve for Y if X is given?
\n" ); document.write( " \n" ); document.write( "
Algebra.Com's Answer #296106 by htmentor(1343)\"\" \"About 
You can put this solution on YOUR website!
Assume the formula is a quadratic of the form \"y+=+ax%5E2+%2B+bx+%2B+c\"
\n" ); document.write( "The following (x,y) points lie on the curve:
\n" ); document.write( "x y
\n" ); document.write( "1 2
\n" ); document.write( "2 4
\n" ); document.write( "3 7
\n" ); document.write( "4 11
\n" ); document.write( "5 16
\n" ); document.write( "Now we need to find the coefficients, a, b and c.
\n" ); document.write( "Using the first 3 points, we can generate a system of 3 equations with 3 unknowns:
\n" ); document.write( "(1) 2 = a + b + c
\n" ); document.write( "(2) 4 = 4a + 2b + c
\n" ); document.write( "(3) 7 = 9a + 3b + c
\n" ); document.write( "Solve for c in (1): 2 - a - b = c
\n" ); document.write( "Substitute into (2) and (3):
\n" ); document.write( "4 = 4a + 2b + (2 - a - b) (4)
\n" ); document.write( "7 = 9a + 3b + (2 - a - b) (5)
\n" ); document.write( "Now solve for b in terms of a in (4): 4 = 3a + b + 2 -> b = 2 - 3a
\n" ); document.write( "Substitute this value for b into (5): 7 = 9a + 3(2 - 3a) + 2 - a - (2 - 3a)
\n" ); document.write( "Solving for a gives a gives 7 = 6 + 2a -> a = 1/2
\n" ); document.write( "From (4), 4 = 4(1/2) + 2b + 2 - 1/2 - b -> 4 = 7/2 + b -> b = 1/2
\n" ); document.write( "Using (1), 2 = 1/2 + 1/2 + c -> c = 1
\n" ); document.write( "So, the formula is \"y+=+%281%2F2%29x%5E2+%2B+%281%2F2%29x+%2B+1\"
\n" ); document.write( "Check using points 4 and 5:
\n" ); document.write( "11 = 1/2(4)^2 + 1/2(4) + 1 = 8 + 2 + 1 = 11
\n" ); document.write( "16 = 1/2(5)^2 + 1/2(5) + 1 = 25/2 + 5/2 + 1 = 16\r
\n" ); document.write( "\n" ); document.write( "\"graph%28300%2C200%2C-10%2C10%2C-20%2C20%2C%281%2F2%29x%5E2+%2B+%281%2F2%29x+%2B+1%29\"\r
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