Parabola

Find the equation of a parabola that contains the points at A[10; -5], B[18; -7], C[20; 0]. (use y = ax²+bx+c)

Correct answer:

a = 0.375
b = -10.75
c = 65

f (x) = a_{x}^{2} + b_{x} + c = y a \cdot 1 0^{2} + b \cdot (10) + c = - 5 a \cdot 1 8^{2} + b \cdot (18) + c = - 7 a \cdot 2 0^{2} + b \cdot (20) + c = 0 100 a + 10 b + c = - 5 324 a + 18 b + c = - 7 400 a + 20 b + c = 0 P i v o t : R o w 1 \leftrightarrow R o w 3 400 a + 20 b + c = 0 324 a + 18 b + c = - 7 100 a + 10 b + c = - 5 R o w 2 - \frac{3 2 4}{4 0 0} \cdot R o w 1 \to R o w 2 400 a + 20 b + c = 0 1.8 b + 0.19 c = - 7 100 a + 10 b + c = - 5 R o w 3 - \frac{1 0 0}{4 0 0} \cdot R o w 1 \to R o w 3 400 a + 20 b + c = 0 1.8 b + 0.19 c = - 7 5 b + 0.75 c = - 5 P i v o t : R o w 2 \leftrightarrow R o w 3 400 a + 20 b + c = 0 5 b + 0.75 c = - 5 1.8 b + 0.19 c = - 7 R o w 3 - \frac{1 . 8}{5} \cdot R o w 2 \to R o w 3 400 a + 20 b + c = 0 5 b + 0.75 c = - 5 - 0.08 c = - 5.2 c = \frac{- 5 . 2}{- 0 . 0 8} = 65 b = \frac{- 5 - 0 . 7 5 c}{5} = \frac{- 5 - 0 . 7 5 \cdot 6 5}{5} = - 10.75 a = \frac{0 - 2 0 b - c}{4 0 0} = \frac{0 - 2 0 \cdot ( - 1 0 . 7 5 ) - 6 5}{4 0 0} = 0.375 a = \frac{3}{8} = 0.375 b = \frac{- 4 3}{4} = - 10.75 c = 65

b = (- 10.75) = - 10.75

c = 65 f (x) = y = a \cdot x^{2} + b \cdot x + c

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