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You can put this solution on YOUR website!
Use the standard form
\n" ); document.write( "(1) y = ax^2 + bx + c
\n" ); document.write( "Substitute (1,-2) into (1) and get
\n" ); document.write( "(2) -2 = a + b + c
\n" ); document.write( "Substitute (2,-2) into (1) and get
\n" ); document.write( "(3) -2 = 4a + 2b + c
\n" ); document.write( "Substitute (3,-4) into (1) and get
\n" ); document.write( "(4) -4 = 9a + 3b + c
\n" ); document.write( "We have three equations and three unknowns. All we need to do is solve for a, b, and c.
\n" ); document.write( "Subtract (3) from (4) and get
\n" ); document.write( "(5) -2 = 5a + b
\n" ); document.write( "Subtract (2) from (3) and get
\n" ); document.write( "(6) 0 = 3a + b
\n" ); document.write( "Now subtract (6) from (5) and get
\n" ); document.write( "(7) -2 = 2a or
\n" ); document.write( "(8) a = -1
\n" ); document.write( "Put (8) into (6) and get
\n" ); document.write( "(9) b = 3
\n" ); document.write( "Put a and b into (2) and get
\n" ); document.write( "(10) c = -4
\n" ); document.write( "Let's check the equation with the three points.
\n" ); document.write( "Is (-2 = -1*1 + 3*1 -4)?
\n" ); document.write( "Is (-2 = -1 + 3 - 4)?
\n" ); document.write( "Is (-2 = -2)? Yes
\n" ); document.write( "Is (-2 = -1*2^2 + 3*2 - 4)?
\n" ); document.write( "Is (-2 = -4 +6 -4)?
\n" ); document.write( "Is (-2 = -2)? Yes
\n" ); document.write( "Is (-4 = -1*3^2 + 3*3 -4)?
\n" ); document.write( "Is (-4 = -9 +9 -4)?
\n" ); document.write( "Is (-4 = -4)? Yes
\n" ); document.write( "Answer: The quadratic function (parabola) that passes through the three given points is -x^2 + 3x -4. By the way, the parabola's apex is (3/2,-7/4)
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