If the parabola y = ax square + BX + C passes through (2,0) (0,2) (- 1,0) 3 points, its analytical formula is

If the parabola y = ax square + BX + C passes through (2,0) (0,2) (- 1,0) 3 points, its analytical formula is

Because the points (2,0), (- 1,0) are on the X axis, the analytic expression of the intersection of the parabola is
y=a(x-x1)(x-x2)
That is y = a (X-2) (x + 1)
Substituting point (0,2) into y = a (X-2) (x + 1) to get 2 = a (0-2) (0 + 1)
a=-1
So the analytical formula of parabola is y = - (X-2) (x + 1)
That is y = - x ^ 2 + X + 2

The square of parabola y = ax + BX + C passes through (- 1, - 22), (0,8), (2,8) three points, and its opening direction, symmetry axis and term point coordinates are obtained

The solution to the problem is a * (- 1) &# + b * (- 1) + C = - 22
a*（0）²+b*（0）+c=-22
a*（2）²+b*（2）+c=8
That is, A-B + C = - 22,
c=8
4a+2b+c=8
The solution is a = - 10, B = 20, C = 8
The parabola is y = - 10x & # 178; + 20x + 8
That is, the opening direction is upward, the axis of symmetry x = 1 and the coordinate of the term point (1.18)

Given that the parabola y = ax square + BX + C passes through points (1,0), (5,0), (0,3) and three points, find the explanatory formula of the parabola

(1,0) (5,0) (5,0) (1,0) (5,0) (5,0) (0,3) (0,3) the three coordinates are substituted into the equations of y = ax square + BX + C, which are 0 = 1A + 1b + C, 0 = 1A + 1b + C, 5,0,0 (0,3) (3,3) the three coordinates are substituted into the equations of y = ax square + BX + C, respectively 0 = 0 = 0 = 1A + 1b + C, 0 = 0 = 1A + 1b + 1b + 5B + C, C = 3, C = 3, C = 3 (0,3 = 25A + 5B + 3 = 25A + 5b, the-3 = 3 + 3 + 3 + 3 + 3 + 3 + 3 + 3 = 25A + 25A + 3 + 3 + 3 + 3 + 5, the-3 + 3 + 3 + X + X + 3, so the y = x square + x square + X + x + X + X + X is the y = y = 3 = 3 = 3 6x + 3

The square of parabola y = ax + BX + C passes through the vertex coordinates B (2, - 1 / 2) of point a (1,0) to find the value of a, B, C?

Let y = a (X-2) & #178; - 1 / 2. Substitute x = 1, y = 0 into a = 1 / 2, so y = 1 / 2x & #178; - 2x + 3 / 2.. so a = 1 / 2, B = - 2, C = 3 / 2