The analytic expression of quadratic function is determined according to the condition, Over three points (1,0), (5,0) and (2, - 3) If we use the analytic expression of quadratic function, we can't solve it,

The analytic expression of quadratic function is determined according to the condition, Over three points (1,0), (5,0) and (2, - 3) If we use the analytic expression of quadratic function, we can't solve it,

According to the intersection formula of the analytic formula of quadratic function, we can assume that the analytic formula of quadratic function is y = a (x-1) (X-5)
Because: the analytic expression of quadratic function passes through point (2, - 3)
So: - 3 = a (2-1) (2-5), the solution is: a = 1
So: the analytic expression of quadratic function is y = (x-1) (X-5), that is, y = x ^ 2-6x + 5

Quadratic function. Find the analytic expression satisfying the following conditions
1. It is known that the vertex of the parabola is at the origin and passes through (5.2)
2. Quadratic function y = - x2 + BX + C. when x = 1, y = 0, when x = 4, y = = 21

1. Let the analytic formula of parabola be y = ax & sup2;
∵ parabolic crossing point (5,2)
The analytic formula of the parabola is y = 2 / 25X & sup2;
2. ∵ when x = 1, y = 0, when x = 4, y = 21
∴0=-1+b+c
21=-16+4b+c
∴b=12 c=-11
The analytic expression of quadratic function is y = - X & sup2; + 12x-11

According to the following conditions, the analytic expressions of quadratic functions are obtained respectively
(1) It is known that the image of quadratic function passes through the point (- 2, - 1), and when x = - 1, the function has the maximum value of 2;
(2) It is known that the symmetry axis of quadratic function image is a straight line x = 1, which intersects the coordinate axis at points (0, - 1), (- 1,0)
Just do the second question

2) If y = ax ^ 2 + BX-1, then y = ax ^ 2 + BX-1
If y (1) = a + B-1 = 0, then a + B = 1
If the axis of symmetry is a straight line x = 1, then - B / (2a) = 1, then B = - 2A
The simultaneous solution is: a = - 1, B = 2
So y = - x ^ 2 + 2x-1