Middle School Mathematics about function problems in detail.

1) The intersection of the straight line y=3x-1 and y=x-k is in the fourth quadrant. From the relation y=3x-1, we can see that this function goes through the first.

I. 3. Fourth quadrant. As can be seen from the relation y=x-k (the coefficient of x is greater than 0), this function must have passed through the first.

1. The third quadrant. And these two straight lines are compared in the first quadrant, so y=x-k also passes through the first.

I. 3. Fourth quadrant. From this we can see that the coefficient of k is -1, and if -k is greater than 0, this function passes through the first.

I. 2. The third quadrant. So -k is less than 0

k<0

y=3x-1 y=x-k ∴3x－1＝x－k ∴x＝(1－k)/2 y＝(1－3k)/2

The intersection is in the fourth quadrant (1 k) 2 0 (1 3k) 2 0 1 3 k 1

The image of the primary function y=ax+b is excessive.

1, 2, 4 quadrants, and intersect with the x-axis with the point (2,0).

a＜0 b＞0 2a＋b＝0 ∴b＝﹣2aa(x－1)－b＞0 ∴a(x－1)＞b ∵a＜0 ∴x－1＜b/a＝﹣2

x＜﹣1

Because y=3x-1 and y=x-k intersect four quadrants. So the coordinates of the intersection point x>0, y<0That is, (1+k) 2>0 (3k+1) 2<0 So the value range of k is -1 3>k>-1

If the image of y=ax+b passes the quadrant of one, two, four, then a<0,b>0 and the image passes (2,0)2a+b=0a(x-1)-b>0 can be reduced to ax>a+b solution to x, so x, <-a a, i.e., x<-1

There are two types of junior high school functions: "one is the primary function y=kx+b, and the other is the quadratic function y=ax 2+bx+c."

Just look at the book; The key is understanding.

Cross multiplication is the method of factoring.

Question 1: What you need to know is:

Suppose the other intersection is d

Then there must be an ABCD four-point common hidden modulus circle.

Then the value of ao*bo is x1*x2*(-1) of x 2+bx+c=0

x1*x2 is equal to c

So ao*bo is equal to -c

Then do*oc=do* -c

and ao*bo=do*oc

So d(0,1) is a fixed point.

Question 2: First: OC AO=OB OC Because ACB is a right angle, AOC is similar to COB

Then oc 2=ao*ob=-c

oc=-c again

So c 2 = -c

Use the root finding formula:

It is obtained that c is equal to 0 or -1

0 This value attack has to be given up.

So c(0,-1).

Then ab=4

So pb=2

Because the beat is a function of x 2.

pb=2 then the same 2 2=4

So pm=4

Then cn=pm-oc=4-1=3

Relative m:

cn is mn2

Then mn = root number 3

The coordinates of p are (-2 b,0).

That's (-2 b, 0).

2/b is equal to root number 3

Then b is equal to 2 root number 3

Because b can be taken as a negative number.

So b is equal to plus or minus 2 root number 3

To sum up: b = plus or minus 2 root number 3

c=-1 <>

1) According to the title, be= 12bp, be= 12x, ec= 4-12x

and fc = 12ec, fc = 2- 14x, af = 4-fc = 2 + 14x

aq = 12af, aq = 1 + 18x, the functional relationship between y and x is y=1 + 18x

2) The point p coincides with the point q, x+y=4, x+1+ 18x=4, and the solution is x= 83, when the length of bp is equal to 83, the point p coincides with the point q

Comments: This question is a comprehensive question, not very difficult, mainly to test in the right triangle, the right angle of 30° is equal to half of the hypotenuse

Solution: The vertex coordinates of the image of the quadratic function are (-1,2), and the analytical formula can be y=a(x+1) +2

Because the parabola passes through the point (1,-3).

3=a(1+1)²+2

a=-5/4

So the parabolic analytic formula is y=-5 4(x+1) +2

The vertex is (-1,2) is symmetrical with respect to the line x=-1, and after (1,-3), it is (-3,-3), and let the square of the function f(x)=ax + bx+c, and bring the three points in, and we can solve a=-5 4, b=-5 2, c=3 4

Use the vertex formula to solve: let the analytic formula of the function be y=a(x+1) +2, and substitute x=1, y=-3 to get :

3=a(1+1)²+2

4a=-5a=-5/4

Then the analytic formula of the function is: y=-5 4(x+1) +2

With the vertex formula, bring in the vertex to get y=a(x+1)2+2

Then bring the points (1, -3) into the solution to get a=-5 4

So the quadratic formula is y=-5 4(x+1) +2=-5 4x2-5 2x+3 4

This is a problem with parabolic equations.

According to the vertex coordinates, it can be assumed that the quadratic function relation is y-2=a(x+1), then according to the image passing point (1,-3), bring this point into the equation to get -5=a 4 to get a=-5 4=-5 4

So the quadratic function relation is y-2=-(5 4)(x+1) and you can simplify it a little more.

Place the parabola y=2x -4x

5. Rotate 180° around the vertex, then the vertex and the axis of symmetry will not change, but the direction of the parabolic opening will change, and the coordinates of the intersection of the parabola and the y-axis will change.

i.e.: y=2x -4x

5. None of the above answers are correct.

I choose D, thank you for adopting!

，0）b（0，3）

AB is y=-3 4x+3

2.Respectively cross the point P to make perpendicular lines with the x-axis and y-axis.

From the similarity to P (4t 5, 3-3t 5).

s aop = 1 2·oa·h = 1 2·4·(3-3t 5)=-6t 5+6 (0 0 no solution does not exist.

In fact, the problem is to figure out what a vertex is, that is, when x takes a certain value, y has a minimum value, so y = (x) squared - 2x-1

Converted to y=(x-1) 2-2, when x=1, y has a minimum value of -2, so this is his vertex coordinates (1,-2).

The coordinates of its intersection with the x-axis mean that when y=0, x=?Of course, if you solve the equation (x-1) 2-2=0, this should be, right? There are 2 solutions to the quadratic equation, so the answer comes out, and the solution is x1=1+2

x2=1-2, is the meaning of the square root, this regular square root, the computer is not very easy to input, you can understand it, if you can draw a commonly used curve graph, you know this type of graph, there must be a minimum value (vertex), there is no focus, this depends on whether 4ac-b 2 4a is greater than 0, three cases, you can analyze it yourself, 4ac-b 2 4a this is a mathematical formula, if you are not clear, you have to read the book.

The formula for vertex coordinates is as follows: y=ax 2+bx+c

Then the vertex coordinates are (-b 2a,4ac-b 2 4a), so the vertex coordinates of the quadratic function y=x 2-2x-1 are (1,-2), and the coordinates of its intersection with the x-axis are when y is 0.

That is to solve a binary equation.

x^2-2x-1=0

The solution is x1 = 1 + 2

x2=1-√2

So the coordinates of its intersection with the x-axis are: (1+ 2,0) and (1- 2,0).

Although I don't know if you are the answer from **, but it should be wrong, there are two ways for your reference:

1. Numerical method: m).

2. Image method: In the velocity and time image, the distance made by the object is numerically consistent with the area enclosed by the image, so the trapezoidal area, that is, the distance = (120 + 135) 5 2 = meters).

<> wish you progress in your studies and reach a higher level! If you don't understand, please keep an eye on it in time to ask, and be satisfied with Jing Kai Crack Mountain, o( o Thank you

Remember and the first price, it is not easy to answer the question, I hope our labor can be recognized, which is also the motivation for us to continue to move forward!

Substituting p((y=-ax+3 to get x=1 a, let p(1 a,2) into the parabolic equation to solve a=1, and then let the two potato equations of the simultaneous two potato equations to find the coordinates of exactly two points.