Given the plane rectangular coordinate system xoy, the parabola y = - x2 + BX + C passes through points a (4,0), B (1,3). (1) find the expression of the parabola, and write out the symmetry axis and vertex coordinates of the parabola; (2) note that the symmetry axis of the parabola is a straight line L, let the point P (m, n) on the parabola be in the fourth quadrant, the symmetry point of point P about line L is e, and the symmetry point of point e about y axis is f, if The area of oapf is 20, and the values of M and N are obtained

Given the plane rectangular coordinate system xoy, the parabola y = - x2 + BX + C passes through points a (4,0), B (1,3). (1) find the expression of the parabola, and write out the symmetry axis and vertex coordinates of the parabola; (2) note that the symmetry axis of the parabola is a straight line L, let the point P (m, n) on the parabola be in the fourth quadrant, the symmetry point of point P about line L is e, and the symmetry point of point e about y axis is f, if The area of oapf is 20, and the values of M and N are obtained

(1) Substituting the coordinates of a (4,0) and B (1,3) into the equation of parabola, we can get: - 42 + 4B + C = 0-12 + B + C = 3, the solution is: B = 4, C = 0; so the expression of parabola is: y = - x2 + 4x, and the expression formula of parabola is: y = - x2 + 4x = - (X-2) 2 + 4, so the straight line of symmetry axis is a straight line x = 2, and the vertex coordinates are (2,4); (2) the symmetry point of point P (m, n) with respect to the straight line x = 2 If it is marked as point E (4-m, n), then point E is symmetric about y axis, and f coordinate is (M-4, n), then FP = OA = 4, that is, FP and OA are parallel and equal, so quadrangle oapf is parallelogram; s = OA ·| n | = 20, that is, | n | = 5; because point P is the point of the fourth quadrant, so n < 0, so n = - 5; substituting into parabolic equation, M = - 1 (rounding off) or M = 5, so m = 5, n = - 5

As shown in the figure, in the plane rectangular coordinate system, it is known that the parabola y = ax & sup2; + Ba + C intersects the X axis at a (2,0), B (6,0)
As shown in the figure, in the plane rectangular coordinate system, it is known that the parabola y = ax & sup2; + Ba + C intersects the x-axis at two points a (2,0), B (6,0), and the y-axis at point C (0,2 √ 3). (1) find the analytical formula of the parabola, (2) if the symmetric axis of the parabola intersects the straight line y = 2x at point D, make the circle D tangent to the x-axis, and the circle D intersects the y-axis at two points E and F, find the length of the inferior arc EF, (3) P is a point of the parabola in the second quadrant image, PG is perpendicular to the x-axis, the perpendicular is point G, try to determine the position of point P, so that the area of △ PGA is divided into two parts of 1:2 by the straight line AC

It's BX, right?!