A mathematical problem of quadratic function in junior high school Parabola y = AX2 + BX + C, vertex coordinates of passing point a (- 3,0) B (1,0) C (0, √ 3) are d. find out whether there is a point P on the straight line BC, so that the perimeter of triangle pad is minimum. If there is, find out the coordinates of point P, and explain why there is no such point

Because of C (0, √ 3), C = √ 3, y = ax ^ 2 + BX + √ 3, a and B are brought into 9a-3b + √ 3 = 0A + B + √ 3, the equation is solved to get a = - (√ 3) / 3B = - (2 √ 3) / 3Y = - (√ 3) x ^ 2 / 3 - (2 √ 3) x / 3 + √ 3, so vertex D abscissa-b / 2A = - 1, so d [- 1, (4 √ 3) / 3], and then the equation of straight line ad is listed: y = (2 √ 3) / 3

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