It is known that the fixed point of the parabola y = ax square + BX + C is on the x-axis, and the intersection point of the parabola and the y-axis is B (0,1), and B = - 4ac. I have found that the analytical formula of the parabola is y = 1 / 4x plane It is known that the fixed point of the parabola y = ax square + BX + C is on the x-axis, and the intersection point with the y-axis is B (0,1), and B = - 4ac I have worked out the parabola analytic formula as Y = 1 / 4x square - x + 1 Points B (0,1), a (2,0) Is there C on the parabola? A circle with diameter BC passes through vertex a? C coordinate and center P are requested! (3) On the basis of (2), the relationship between abscissa and ordinate of B, P and C is analyzed

It is known that the fixed point of the parabola y = ax square + BX + C is on the x-axis, and the intersection point of the parabola and the y-axis is B (0,1), and B = - 4ac. I have found that the analytical formula of the parabola is y = 1 / 4x plane It is known that the fixed point of the parabola y = ax square + BX + C is on the x-axis, and the intersection point with the y-axis is B (0,1), and B = - 4ac I have worked out the parabola analytic formula as Y = 1 / 4x square - x + 1 Points B (0,1), a (2,0) Is there C on the parabola? A circle with diameter BC passes through vertex a? C coordinate and center P are requested! (3) On the basis of (2), the relationship between abscissa and ordinate of B, P and C is analyzed

Question 3 should be answered first
Because P is the center of the circle and BC is on the circle, so BP = PC, because BC is the diameter, so p is the midpoint of BC
Because B is on the Y axis, the X coordinate of C is twice that of P
At the same time: CY py = py by
Question 2:
Calculate the slope of the straight line Ba, because BC is the diameter and a is on the circumference, so the angle BAC = 90 degrees, that is, Ba is perpendicular to AC,
That is to say, the slope of AC line can be obtained by perpendicular to ab
The intersection point of AC line on X axis is a point, which is the intercept on X axis. Then we can get the linear equation of AC and find the intersection point with parabola
We get the C coordinate
Then use the answer of question 3 to get the coordinates of the center P

It is known that: as shown in the figure, the parabola y = AX2 + BX + C intersects with the X axis at two points a (1,0), B (3,0), and intersects with the Y axis at point C (0,3). (1) find the functional relation of the parabola; (2) if the point d (72, m) is a point on the parabola y = AX2 + BX + C, ask for the value of M, and find out the area of △ abd at this time

(1) It is known that a + B + C = 09A + 3B + C = 0C = 3, (3 points) the solution is a = 1b = − 4C = 3, (4 points) ∵ y = x2-4x + 3; (5 points) (2) ∵ D (72, m) is a point on the parabola y = x2-4x + 3, ∵ M = 54; (6 points) ∵ s △ abd = 12 × 2 × 54 = 54. (8 points)