The properties of linear function The relation of the following functions is expressed analytically, and its independent variable and dependent variable are pointed out 1. Suppose that the surface temperature is 30 degrees centigrade. When it is not higher than 12 km, if it increases by 1 km, the temperature will decrease by 6 degrees centigrade. Write out the functional relationship between the air temperature T and the height H 2. A kind of push-pull rectangular plastic window, the length is 862 mm, the maximum width is 475 mm when it is opened. If the opening width is x mm, the area of the opening part s square mm is the function of the opening width? (find the domain of definition)

The properties of linear function The relation of the following functions is expressed analytically, and its independent variable and dependent variable are pointed out 1. Suppose that the surface temperature is 30 degrees centigrade. When it is not higher than 12 km, if it increases by 1 km, the temperature will decrease by 6 degrees centigrade. Write out the functional relationship between the air temperature T and the height H 2. A kind of push-pull rectangular plastic window, the length is 862 mm, the maximum width is 475 mm when it is opened. If the opening width is x mm, the area of the opening part s square mm is the function of the opening width? (find the domain of definition)

（1）T = 30 + 6H (H≤12km)
(2)
S = 862×X
= 862X (X≤475mm)

It is known that the first-order function image of X passes through the point (2,4) and the ordinate of the intersection point with the y-axis is - 2 (1). Find the function relation of Y with respect to X

Let y = KX + B
Over (2,4)
4=2k+b
X = 0 on y-axis
So x = 0, y = - 2
Then - 2 = 0 + B
b=-2
k=(4-b)/2=3
So y = 3x-2

It is known that the image of the function y = MX + n passes through (- 1,4), and the ordinate of the intersection point with the y-axis is - 2. The function relation is

Let x = O, y = - 2 get n = - 2, so y = mx-2
Let x = - 1, y = 4 give M = - 6
y=-6x-2

Given that the image of a function passes through a (2, - 1) and point B, where B is the intersection of another straight line y = - 0.5x + 3 and Y axis, the analytic expression of the function is obtained

The intersection of y = - 0.5x + 3 and Y axis
Let x = 0
y=-0.5*0+3=3
Intersection (0,3)
Let the primary function be y = KX + B
-1=2k+b
3=0*k+b
b=3
k=(-1-b)/2=-2
y=-2x+3

It is known that the image of a linear function passes through a (2, - 1) and point B, where point B is the intersection of another straight line y = 5x + 3 and Y axis. The analytic expression of this linear function is obtained
It is known that the image of a linear function passes through a (2, - 1) and point B, where point B is the intersection of another line y = 5x + 3 and Y axis
Find the analytic expression of this first-order function:

y=kx+b
-1=2k+b
y=kx-2k-1
Intersection y = 0 x = - 3 / 5
0=-3k/5-2k-1
k=5/13
Linear equation y = 5x / 13-23 / 13

Mathematical problems in the fourth grade of junior high school
1. The analytic formula of parabola with vertices (- 2, - 5) and passing through points (1, - 14) is________
2. The analytical formula of the parabola passing through a (1,3) B (- 2, - 6) is________
3. The length of the line cut by the parabola y = - 2x & sup2; + 4x + 1 on the x-axis is_______
4. If the vertex of the parabola y = x & sup2; + (m-2) x + (M & sup2; - 4) is at the origin, then M=________
5. Parabola y = - X & sup2; - 2x + m, if its vertex is on the X axis, then M=________
6. Given the quadratic function y = (m-1) x & sup2; + 2mx + 3m-2, then=____ The maximum value is 0
7. The condition that the value of quadratic function y = ax & sup2; + BX + C is always negative is a____ 0,b²-4ac_____ zero

1.Y =-(X+2)^2-5
2.Y = X^2 + 2
three point four
four point two
five point one
6.1/2
7.<

The graph of a quadratic function intersects with X axis at points [- 1,0], [4,0], and its shape is the same as that of y = - x2
In y = - X2, 2 means square

From "the image of the quadratic function: y = ax & # 178; + BX + C (a, B, C are constants, and a is not equal to 0) is the same as that of y = - X & # 178;", it is obtained that the coefficient of the quadratic term of the quadratic function is also - 1, that is, a = - 1