Quadratic function and quadratic equation of one variable! 1. The number of intersections of quadratic function y = 2 (x + 2) (x-1) and x-axis is -- and the coordinates of the intersections are—— 2. When m -- the parabola y = x ^ - x + m has an intersection with the X axis 3. If the quadratic function y = 3x ^ + 3x-6 has an intersection with the x-axis, and the coordinates of the intersection are -, then we can see that the quadratic equation 3x ^ + 3x-6 = 0 has a solution, that is, the solution is - 4. Given quadratic function y = 2x ^ - (M + 1) x + (m-1) (1) It is proved that no matter what the value of M is, the image of function y always has an intersection with X axis, and it is pointed out that when the value of M is, there is only one intersection with X axis 5. It is known that the parabola y = ax ^ + 4x + 3 has only one intersection point a with the X axis, and the intersection point with the Y axis is B. try to find the coordinates of a and B and the length of the line ab 6. Given that the image of quadratic function y = x ^ - 2x-3 intersects with X axis at points a and B, there is a point C on the parabola above X axis, and the area of triangle ABC is 10, the coordinate of point C is obtained One two three questions only need to give the result directly. Four five six three questions need the concrete process

Quadratic function and quadratic equation of one variable! 1. The number of intersections of quadratic function y = 2 (x + 2) (x-1) and x-axis is -- and the coordinates of the intersections are—— 2. When m -- the parabola y = x ^ - x + m has an intersection with the X axis 3. If the quadratic function y = 3x ^ + 3x-6 has an intersection with the x-axis, and the coordinates of the intersection are -, then we can see that the quadratic equation 3x ^ + 3x-6 = 0 has a solution, that is, the solution is - 4. Given quadratic function y = 2x ^ - (M + 1) x + (m-1) (1) It is proved that no matter what the value of M is, the image of function y always has an intersection with X axis, and it is pointed out that when the value of M is, there is only one intersection with X axis 5. It is known that the parabola y = ax ^ + 4x + 3 has only one intersection point a with the X axis, and the intersection point with the Y axis is B. try to find the coordinates of a and B and the length of the line ab 6. Given that the image of quadratic function y = x ^ - 2x-3 intersects with X axis at points a and B, there is a point C on the parabola above X axis, and the area of triangle ABC is 10, the coordinate of point C is obtained One two three questions only need to give the result directly. Four five six three questions need the concrete process

Two, (1,0), (- 2,0) m ≤ 1 / 4 (1,0), (- 2,0); X1 = 1. X2 = - 2Y = 2x ^ - (M + 1) x + (m-1) & nbsp; △ = (M + 1) & # 178; - 4 × 2 × (m-1) & nbsp; & nbsp; = M & # 178; - 6m + 9 = (M-3) & # 178; ≥ 0, so there is always an intersection point; when m = 3, there is only one intersection point

Y = 4x + 1, y = - 4x + 1, y = 4x + 1 the list of drawing function image
Y = 4x + 1 y = - 4x + 1 y = 4x + 1 how to calculate the number in the list when drawing function image

You can find any number of generations, such as x = 0, y = 1

Y = - 4x draw the function image

When x = 0, y = 0
When x = 1, y = - 4
Find the line connecting the two points
This can be recommended

If the image of quadratic function y = AX2 + BX + C (a = / 0) is as shown in the figure, (the opening is upward, and the vertex is in the fourth quadrant), then the line y = bx-c does not pass through the fourth quadrant

Because the opening is up
So a > 0
Because the vertex is in the fourth quadrant
So the axis of symmetry x = - B / 2A > 0
So B0, y = bx-c does not pass through the first quadrant
If the intersection of the image and the y-axis is on the negative half axis of Y, then C

In order to make the image of function y = (2m-3) x-3m + 1 pass through two three four quadrants, the values of M and n should be

K=2m-3

Mr. Wang asked the students to consider a linear function. Please give a property to this function
A: the function image passes through the second quadrant and does not pass through the third quadrant
B: when x > 0, y < 0
C: y decreases with the increase of X
D: when x = - 2, y = 3
Please write out the functional relationship suitable for the above four conditions

Let the first-order function y = ax + B
When x ＞ 0, y ＜ 0, it means that the function image passes through the fourth quadrant
So the image is in quadrant two or four, so B = 0
When x = - 2, y = 3
3 = - 2A, a = - 3 / 2
Function relation: y = - 3 / 2x

Mr. Zhang gave a function y = f (x), and four students pointed out a property of this function
The teacher gave a function graph y = f (x), and four students pointed out the properties of this function
A: for the graph where x belongs to R function, it is symmetric with respect to the straight line x = 1
B: on (- infinity, 0), the function decreases
C: increasing function on (0, + infinity]
D: F (0) is not the minimum of a function
Can the answer be y = - x ^ 2-1?

y=-x^2-1
A: for the graph where x belongs to R function, it is symmetric with respect to the straight line x = 1
B: on (- infinity, 0), the function decreases
C: increasing function on (0, + infinity]
It doesn't match
Only D: F (0) is not the minimum value of a function. F (0) = - 1, where y is smaller than - 1, there is an infinite number
So can't the answer be y = - x ^ 2-1?
I feel that there is something wrong with the topic. It is impossible to meet all four conditions

The teacher gives a function y = f (x), and four students a, B, C and D point out a property of the function: A: Yes
The teacher gives a function y = f (x), and four students a, B, C and D point out a property of this function: A: for X ∈ R, f (1 + x) = f (1-x); B: on (- ∞, 0), the function increases; C: on (0, + ∞), the function increases; D: F (0) is not the minimum value of the function
If three of them are right, write a function like this

A: it shows that the function is symmetric with respect to x = 1
B: the function increases in the negative half of X
C: the function increases in the positive half of X
D: F (0) is not the minimum
Obviously, if a is right, because of the symmetry, then B and C must be wrong. But also because the symmetry axis is x = 1, it is impossible to increase or decrease in a certain x half region (only x = 1 as the boundary)
Therefore, only a is incorrect. The other three are correct. For example, y = x ^ 3

Write a function satisfying the following conditions: (1) its image is a straight line passing through the origin; (2) y increases with the increase of X

The results are as follows: 1
A positive proportional function
The results are as follows (2)
K>0
example:
y=5x
y=2.5x
Baidu Hi~

What are the properties of two function images about the origin symmetry
What is the necessary and sufficient condition? How to deduce one from another?

Y = f (x) and y = - f (x) are symmetric about the X axis
Y = f (x) y = (- x) about Y-axis symmetry
Y = - f (- x) and y = f (x) are symmetric about the origin