It is known that the parabola y = AX2 + BX + C passes through the point (- 1,2) and the roots of the equation AX2 + BX + C are - 3,1 respectively Solving the parabola analytic formula Finding the coordinates of parabola vertex | Math enthusiast | Mathematical art

It is known that the parabola y = AX2 + BX + C passes through the point (- 1,2) and the roots of the equation AX2 + BX + C are - 3,1 respectively Solving the parabola analytic formula Finding the coordinates of parabola vertex

∵ 2 = A-B + C0 = 9a-3b + C0 = a + B + C = > - 2 = 2B [(3) - (1)] = > b = - 10 = 8a-4b [(2) - (3)] = > A = - 1 / 2 = > C = - A-B = 1 / 2 + 1 = 3 / 2 ∵ the analytical formula of the parabola is y = - (1 / 2) x ^ 2-x + 3 / 2, the vertex coordinates are (- B / 2a, [4ac-b ^ 2] / 4A) = > (- 1,2)

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1. If the axis of symmetry of the parabola y = AX2 + BX + C (a ≠ 0) is a straight line x = 2 and the minimum value is - 2, then the root of the equation AX2 + BX + C = - 2 about X is______ ．
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