## If the straight line L and the straight line y = 2x + 1 are symmetrical about the Y axis, the analytical formula of the straight line L is

Because of symmetry about the y-axis

So the Y coordinate is the same and the X coordinate is the opposite

Substitute - x = x into the line

Y = - 2x + 1 is the required value

### It is known that the straight line L and the straight line y = - 3x + 2 intersect at the same point on the Y axis and pass through the point (2, - 3). Find the functional analytical formula of the straight line L

Because y = - 3x + 2 and intersects the Y axis! Therefore, the abscissa of the intersection x = 0 is directly substituted into the above formula y = 2, so the intersection is (0,2) and because it passes through the point (2, - 3), the equation L is 5x + 2y-2 = 0

### Find the functional relationship of the line y = 3x-2 with respect to the line with Y-axis symmetry

The ordinates of the y-axis symmetric points remain unchanged, and the abscissa are opposite to each other. Therefore, the functional relationship of the straight line y = 3x-2 with respect to the y-axis symmetric straight line is: y = - 3x-2

### If the straight line L and the straight line y = 3x + 2 are symmetrical about the X axis, what is the analytical formula of the straight line l?

The line L and y = 3x + 2 are symmetrical about the X axis

Is all the points (x, y) above L, and the corresponding points (x, - y) about X are on y = 3x + 2

So - y = 3x + 2

That is, y = - 3x-2

Let the equation of l y = f (x)

Then (x, y) is the point on L

The symmetry point of (x, y) about the X axis is (x, - y) on the line y = 3x + 2

So - y = 3x + 2

Then y = - 3x-2

### As shown in the figure, the image of quadratic function y = x2 + BX + C has only one common point P with X The image of the quadratic function y = x2 + BX + C has only one common point P with the x-axis, and the intersection with the y-axis is Q. find the analytical formula of the quadratic function The image of the quadratic function y = x2 + BX + C has only one common point P with the X axis, and the intersection with the Y axis is Q. the straight line y = 2x + m passing through the point Q intersects the X axis at point a and the image of the quadratic function at another point B. if s △ bpq = 3S △ Apq, find the analytical formula of the quadratic function

If there is only one intersection with the X axis, it means that when x = - B / 2, y has the maximum value - B ²/ 4+c=0

The point Q coordinate is (0, c) C = B ²/ four

The straight line y = 2x + m passes through point Q (0, c), so the straight line can be written as y = 2x + C

① solving equations y = 2x + C

y=x ²+ BX + C ② available point B coordinates (2-B, b) ²/ 4+4-2b)

Because s △ bpq = 3S △ Apq, that is, s △ APB = 4S △ Apq,

So the ordinate of B is four times that of Q, that is

b ²/ 4+4-2b=b ² Solution B = - 4 or 4 / 3

So the quadratic function is y = X ²- 4X + 4 or y = x ²+ 4x/3+4/9

### As shown in the figure, it is known that the vertex coordinates of the quadratic function image are (2,0), and the line y = x + 1 and the quadratic function image intersect at two points a and B, where point a is on the Y axis

Therefore, the analytical formula of the quadratic function is y = 1 / 4 x ^ 2-x + 1. \ x0d2. Assuming that the point (- m, 2m-1) is on the quadratic function image obtained in (1), it satisfies 1 / 4 (- M) ^ 2 + 2 * (- M) + 1 = (2m-1) ^ 2. Therefore, the point (- m, 2m-1) is not on the quadratic function image obtained in (1). \ x0d3, (1) y axis