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As shown in the figure, the parabola passes through three points a (4,0), B (1,0), C (0, - 2). (1) find the analytical formula of the parabola (2) There is a point on the parabola above the line AC (3) P is a moving point on the parabola, passing through P as the PM ⊥ X axis, and the perpendicular foot is m. is there a point P, so that the triangle with vertices a, P, and M is similar to △ OAC? If it exists, the coordinates of the qualified point P are requested; if it does not exist, please explain the reason
(1) Using the intersection formula y = a (x-x1) (x-x2) to get y = a (x-4) (x-1), and substituting (0, - 2) into y = a (x-4) (x-1), we get a = - 1 / 2. That is to say, the parabolic equation y = - 1 / 2 (x-4) (x-1) (2) has a point P, let P (x, y) where y is not equal to 0, (because △ APM can not be formed when it is equal to 0)
As shown in the figure, the parabola passes through three points a (4,0), B (1,0) and C (0, - 2). (1) the analytical formula of the parabola is obtained
(2) P is a point on the parabola, passing through P as PM ⊥ X axis, perpendicular to M. is there a P point, so that the triangle with a, P, m as vertices is similar to △ OAC? If it exists, request the P coordinate of the point that meets the conditions; if it does not exist, please explain the reason. (3) there is a point D on the parabola above the straight line AC, so that the area of △ DCA is the largest, so it is not necessary to calculate the D coordinate of the point
(1) Let the quadratic function be y = ax ^ 2 + BX + C and substitute a (4,0) B (1,0) C (0, - 2) to get a = - 1 / 2, B = 5 / 2, then y = (- 1 / 2) x ^ 2 + (5 / 2) X-2 (2) (2) suppose existence, let P (x, y) then: when p is on the left side of the axis of symmetry, that is, (1
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