In the plane rectangular coordinate system, translate the parabola to the right y = x + 6x + 8 to make it pass through the origin, and write an analytical formula of the parabola after translation!

When y = 0, x = - 2 or - 4. Therefore, the image must be shifted two or four units to the right before it can pass through the origin. In order to get the moving image, the first step is to change the image to the form of y = (x + a) square + B. this problem can be reduced to y = x square + 6x + 9-1 and y = (x + 3) Square-1

Translate the parabola y = x & # 178; + 2x-8, make it pass through the origin, and write a relation ()

For parabola y = (x-a) ² + B
If the image crosses the origin
Then, a & # 178; + B = 0, that is, B = - A & # 178;
Therefore, the relation of parabola after translation is y = (x-1) &# 178; - 1 = x & # 178; - 2x

It is known that the square of the parabola y = ax - BX + C (a is not equal to 0) intersects with the x-axis at point C (0,4), and intersects with the x-axis at two points a and B, and the coordinates of point a are (4,0)
Find the expression!
Intersection with Y-axis at point C (0,4)

The axis of symmetry is x = - (- 2A) / (2a) = 1, and there are two different intersections between the parabola and the X axis. These two intersections must be axisymmetric with respect to the axis of symmetry x = 1. Then the coordinates of point B are (- 2,0). Will you do it next?

In the plane rectangular coordinate system XYZ, it is known that the parabola passes through points a (0,4), B (1,0), C (5,0), and the axis of symmetry L and X of the parabola intersect at point M
(3) Connect AC, explore whether there is a point n on the parabola below the straight line, which is the largest area of △ NCA? Please write the coordinates of N. no, please draw it yourself. Thank you,

The parabola passes through the points B (1,0), C (5,0), & nbsp; obviously, its analytical expression can be expressed in the form of Y & nbsp; = & nbsp; a (x-1) (X-5). Substituting the coordinates of a (0,4), we can get the length of a = & nbsp; 4 / 5Y & nbsp; = & nbsp; 4 (x-1) (X-5) / 5 (a) AC

In the plane rectangular coordinate system, translate the parabola to the right y = x + 6x + 8 to make it pass through the origin, and write an analytical formula of the parabola after translation!