The coordinate of the intersection of the image of the first-order function y = - 3K + 1 and the X axis is The intersection coordinate of the image and the Y axis is, and the area of the triangle formed by the image and the two coordinates is

The coordinate of the intersection of the image of the first-order function y = - 3K + 1 and the X axis is The intersection coordinate of the image and the Y axis is, and the area of the triangle formed by the image and the two coordinates is

In the linear function y = - 3x + 1,
When x = 0, y = 1,
Therefore, the coordinates of the intersection of the first-order function y = - 3x + 1 and the Y axis are (0,1);
When y = 0, x = 1 / 3,
Therefore, the coordinate of the intersection of the first-order function y = - 3x + 1 and X axis is (1 / 3,0);
Therefore, the area of the triangle formed by the image and the two coordinates is
S⊿＝1／2×1×1／3＝1／6.

Quadratic function: the square of y = - 2x + 4x + 6 intersects with the x-axis at the coordinate triangle with vertex C of points a and B (a on the left of B)
Quadratic function: y = - 2x square + 4x + 6 and the area of coordinate triangle ABC with X axis intersection at points a and B (a on the left of B) and vertex c c

y=-2（x²-2x+1）+8
=-2（x-1）²+8
We can get that the axis of symmetry is x = 1, the coordinate of fixed point C is (1,8) triangle, and the height of ABC is 8
When y = 0, from X1 = - 1, X2 = 3 of the above formula, namely a (- 1,0), B (3,0), the bottom edge length of ABC is ab = 4
Area: (4 × 8) / 2 = 16

Can the image of y = - 2x ^ 2 + 4x-3 be obtained by the function y = - 2x ^ 2 through translation?
Quadratic function translation

The coefficients of quadratic terms are equal, so they can be used
y=-2x²+4x-2-1
=-2(x-1)²-1
Vertex (1, - 1)
Y = - 2x & sup2; the vertex is the origin
That is, vertices from (0,0) to (1, - 1)
So y = - 2x & sup2; is one unit to the right and one unit to the down

If y = X-1, y = 1 / 4x + 1 / 2, y = - 2x + 5, y = - 1 / 2x + 2 all pass a fixed point, which of the following functions will pass the fixed point

y=x-1=1/4x+1/2
3/4x=3/2
x=2
y=x-1=1
So the first two have passed (2,1)
Substituting the latter two also holds
So the fixed point is (2,1)

If y is a linear function of X, the image passes through the point (- 3,2) and intersects the line y = 4x + 6 at the same point on the x-axis
Finding the analytic expression of the function of degree one

At the same point on the x-axis as the line y = 4x + 6
Straight line passing point (- 1.5,0)
So we can get the analytic formula of the straight line of the point (- 1.5,0), (- 3,2)
We get 4x + 3Y + 6 = 0

The image of the linear function y = - 3 / 4x + 4 intersects the X axis and Y axis at two points ab
1 -------- finding the coordinates of two points ab
2 ------- find the length of line ab
3 ------ whether there is a point C on the x-axis, so that the triangle ABC is an isosceles triangle. If no, please write the coordinates of point C directly. If no, please explain the reason

1. When y = 0, x = 16 / 3, point a (16 / 3,0)
When x = 0, y = 4, B (0,4)
2. Substituting points a and B into y = KX + B, we get
0=16/3k+b
4=b
∴k=-3/4 ,b=4
∴y=-3/4x+4
3. Point C (0,8 / 3),

If the image of a linear function is parallel to the line y = 2x and the intersection X axis is at the point (- 3,0), then the analytic expression of the function is?

Then the intersection of this function is a linear function (- y = 2x) which is parallel to x?
Let the analytic formula be y = 2x + B
(- 3,0) is substituted into: 0 = - 6 + B
b=6
So it is: y = 2x + 6

Given a linear function whose image is parallel to the straight line y = - 1 / 2x, and at the same point as the intersection of the straight line y = 2X-4 and the X axis, the analytic expression of the function is obtained

This problem is divided into three parts
1. Because the image is parallel to the straight line y = - 1 / 2x, we know that its slope is - 1 / 2, so we can set the function as y = - 1 / 2x + B (B represents the unknown number)
2. Because the function and the line y = 2X-4 intersect with the x-axis at the same point, that is, the intersection point of the line y = 2X-4 and the x-axis. According to the characteristic of intersecting with the x-axis, y value is 0, the intersection point can be obtained by substituting the line y = 2X-4, that is, the intersection point of the line y = 2X-4 and the x-axis
0 = 2X-4, the intersection point is (2,0)
3. Because the function also passes this point, substituting (2,0) into y = - 1 / 2x + B, B = 1 can be obtained, so the function is y = - 1 / 2x + 1

Given that the image of a linear function passes through point a (2, - 1) and point B, point B is the intersection of another straight line y = - 1 / 2x + 3 and Y axis, the analytic expression of the linear function is obtained

Because point B is the intersection of another straight line y = - 1 / 2x + 3 and Y axis, the abscissa of point B is 0. That is - 1 / 2x + 3 = 0, the solution is y = 3, so the analytic formula of the first-order function of point B coordinate (0,3) is y = KX + B, and a (2, - 1) and B (0,3) are substituted to get 2K + B = - 1, B = 3, the analytic formula of the first-order function of k = - 2 is y = - 2x + 3

The image of a linear function is parallel to the line y = 2x-5 and intersects with the X axis at (- 2,0)

y=2x＋4