It is known that the image vertex coordinates of the quadratic function are a (- 2,0) and pass B (- 1,2) (find the analytic formula of the quadratic function, let the image intersect with the Y axis at point C, and find the area of △ ABC It is known that the image vertex coordinates of the quadratic function are a (- 2,0) and pass B (- 1,2) (1) to find the analytic formula of the quadratic function. (2) let the image intersect with the Y axis at point C, and find the area of △ ABC

It is known that the image vertex coordinates of the quadratic function are a (- 2,0) and pass B (- 1,2) (find the analytic formula of the quadratic function, let the image intersect with the Y axis at point C, and find the area of △ ABC It is known that the image vertex coordinates of the quadratic function are a (- 2,0) and pass B (- 1,2) (1) to find the analytic formula of the quadratic function. (2) let the image intersect with the Y axis at point C, and find the area of △ ABC

1) If the vertex coordinate is a (- 2,0), then y = a (x + 2) ^ 2
Over B (- 1,2), substituting: 2 = a (- 1 + 2) ^ 2, a = 2
So y = 2 (x + 2) ^ 2
2) When x = 0, y = 8, so C is (0,8)
|AC|=√[(-2)^2+8^2]=2√17
From the intercept formula, the AC equation is: X / (- 2) + Y / 8 = 1
Therefore, the distance from point B to AC H = | - 1 / (- 2) + 2 / 8-1 | / √ (1 / 2 ^ 2 + 1 / 8 ^ 2) = 1 / √ 17
Therefore, the area of ABC = 1 / 2 * | AC | * H = 1 / 2 * 2 √ 17 * 1 / √ 17 = 1

Given that the vertex coordinates of the image of quadratic function is a (- 1,3), the intersection of the image and X axis is at point B and C, and the area of △ ABC is 6, then the analytic expression of the quadratic function is

Let the quadratic function be y = a (x + 1) ^ 2 + 3

The shape, opening direction and symmetry axis of a parabola are the same as the square of y = 2x, and the parabola passes through point (1,1)
(1) The analytic formula of parabola
(2) Find the vertex coordinates of the parabola, and explain how the parabola is obtained by translating the square of y = 2x?

Let the analytic formula of parabola be y = 2x ^ 2 + M
X = 1, y = 1
1=2+m
m=-1
The analytic formula of parabola is y = 2x ^ 2-1
The vertex coordinates of the parabola are (0, - 1)
It is obtained by translating the square of y = 2x down one unit

The axis of symmetry of the parabola y = 2x square + 5 is_______

The symmetry axis of y = 2x ^ 2 + 5 is Y axis