Equation 80525

Write the equation of the parabola that passes through the points: A[1,1] B[3,-1] C[1,2]

Correct answer:

a = 2.5
b = -9.5
c = 8
e : 2,5x^2-9.5x+8=0

A = (1, 1) B = (2, - 1) C = (3, 2) a_{x}^{2} + b_{x} + c = y a \cdot A_{x}^{2} + b \cdot A_{x} + c = A_{y} a \cdot B_{x}^{2} + b \cdot B_{x} + c = B_{y} a \cdot C_{x}^{2} + b \cdot C_{x} + c = C_{y} a \cdot 1^{2} + b \cdot 1 + c = 1 a \cdot 2^{2} + b \cdot 2 + c = (- 1) a \cdot 3^{2} + b \cdot 3 + c = 2 a + b + c = 1 4 a + 2 b + c = - 1 9 a + 3 b + c = 2 P i v o t : R o w 1 \leftrightarrow R o w 3 9 a + 3 b + c = 2 4 a + 2 b + c = - 1 a + b + c = 1 R o w 2 - \frac{4}{9} \cdot R o w 1 \to R o w 2 9 a + 3 b + c = 2 0.667 b + 0.556 c = - 1.889 a + b + c = 1 R o w 3 - \frac{1}{9} \cdot R o w 1 \to R o w 3 9 a + 3 b + c = 2 0.667 b + 0.556 c = - 1.889 0.667 b + 0.889 c = 0.778 R o w 3 - R o w 2 \to R o w 3 9 a + 3 b + c = 2 0.667 b + 0.556 c = - 1.889 0.333 c = 2.667 c = \frac{2 . 6 6 6 6 6 6 6 7}{0 . 3 3 3 3 3 3 3 3} = 8 b = \frac{- 1 . 8 8 8 8 8 8 8 9 - 0 . 5 5 5 5 5 5 5 5 5 5 5 5 5 6 c}{0 . 6 6 6 6 6 6 6 7} = \frac{- 1 . 8 8 8 8 8 8 8 9 - 0 . 5 5 5 5 5 5 5 6 \cdot 8}{0 . 6 6 6 6 6 6 6 7} = - 9.5 a = \frac{2 - 3 b - c}{9} = \frac{2 - 3 \cdot ( - 9 . 5 ) - 8}{9} = 2.5 a = \frac{5}{2} = 2.5 b = \frac{- 1 9}{2} = - 9.5 c = 8

b = (- 9.5) = - 9.5

c = 8

e : e = 2, 5 x^{2} - 9.5 x + 8 = 0

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