The analytic expression y of a quadratic function is equal to x + (M + 5) times the square of X + (M + 2). When m takes any value, there is only one intersection between the function image and X axis

The analytic expression y of a quadratic function is equal to x + (M + 5) times the square of X + (M + 2). When m takes any value, there is only one intersection between the function image and X axis

There is only one intersection point between y = x ^ 2 + (M + 2) x + (M + 5) function image and X axis, which can be regarded as solving equations. The problem is to solve the equations y = x ^ 2 + (M + 2) x + (M + 5) y = 0, that is, x ^ 2 + (M + 2) x + (M + 5) = 0. The number of solutions is the number of intersections, which is also the coordinates of intersections

What is the number of intersections of the parabola y = x & # 178; - 3x + m and X axis?

This problem needs to be discussed by category. It's very troublesome. Wait, I'll type for you
The focus of this parabola and x-axis is the solution of the equation x & # 178; - 3x + M = 0 when y = 0
When △ 0, B &# 178; - 4ac ＞ 0, that is (- 3) &# 178; - 4 × 1 × m ＞ 0, the solution is m ＜ 9 / 4
When △ = 0, B & # 178; - 4ac = 0, that is (- 3) &# 178; - 4 × 1 × M = 0, the solution is m = 9 / 4
When △ 0, B &# 178; - 4ac ＜ 0, that is (- 3) &# 178; - 4 × 1 × m ＜ 0, the solution is m ＞ 9 / 4
To sum up, because a = 1 ＞ 0, the parabolic opening is upward
So when m ＜ 9 / 4, the parabola and X axis have two intersections
When m = 9 / 4, there is an intersection between the parabola and x-axis
When m ＞ 9 / 4, there is no intersection between parabola and X axis

It is known that the vertex of the parabola is (- 1,2), and the quadratic function is obtained through the point (2,1)

It's complicated for the one upstairs. This is the basic exercise of quadratic function in grade three,
Let y = a (X-H) & sup2; + K
Vertex (- 1,2), that is, H = - 1, k = 2, passing through point (2,1), that is, x = 2, y = 1
Put these numbers into this function:
1=a（2+1）²+2
The solution is a = - 1 / 9,
So this function is y = - 1 / 9 (x + 1) & sup2; + 2
Absolutely

Simple equation application problems
When the first engineering team contracted the first project, it took 12 days to complete the project in sunny days and 14% in rainy days. When the second team contracted the second project, it took 15 days in sunny days and 10% in rainy days. In fact, the two teams completed the project at the same time. How many days did the two teams work
When the first engineering team contracted the first project, it took 12 days to complete the project in sunny days, while the project in rainy days decreased by 40%. When the second team contracted the second project, it took 15 days in sunny days, while the project in rainy days decreased by 10%. In fact, the two teams completed the project at the same time. How many days did the two teams work

Let X be sunny and y be rainy, so x / 12 + Y / 12 * (1-40%) = 1 x / 12 + Y / 20 = 1 (1) B be sunny and rainy, so x / 15 + Y / 15 * (1-10%) = 1 x / 15 + 3Y / 50 = 1 (2) (1) * 4 - (2) * 5Y / 5-3y / 10 = - 1y = 10x = 6

It is proved that the tangent lines of a circle drawn from a point outside the circle are equal in length, and the line between the center of the circle and this point bisects the angle between the two tangent lines

Two tangents of a circle from a point outside the circle have the same length. The line between the center of the circle and this point bisects the angle between the two tangents. As shown in the figure, the length of the tangents AC = ab. ∵ {ABO =} ACO = 90 ° Bo = co = radius Ao = Ao common edge ≌ RT Δ ABO ≌ RT Δ ACO (h.l)

Discriminant of quadratic equation with one variable
It is known that a is a real number and the equation x square + 2aX + 1 = 0 has two unequal real roots. This paper tries to judge whether the equation x square + 2aX + 1 + 2 (a Square-1) (x Square-1) = 0 has real roots

b2-4ac=4a2-4=4(a2-1)>0
A 2 - 1 > 0 so a > 1 or a 0 so there are two unequal real roots

What is China's "territory area" and "territory area" in the world?

Land area: Russia first, Canada second, China third
Territorial area
No.1: Russia 17075200
Second: Canada 9984670
No. 3: USA 9629091
4: China 9596960
Number 5: Brazil 8511965

High school physics: the Coulomb force is effective in the range of R = 10 (- 15 power) m ~ 10 (- 11 power) M. why is the Coulomb force invalid when it is greater than a certain distance?
After consulting many books, others say that the Coulomb force is effective in the range of R = 10 (- 15th power) m ~ 10 (- 11th power) M. why is the Coulomb force invalid when it is greater than a certain distance?
It's invalid within 10 (- 15) M. I understand that short distance can't be regarded as point charge, but why can't long distance be regarded as point charge? Beyond the maximum distance, is there no Coulomb force or other formula?
Please don't answer distance, force effect can be ignored, because no matter how small the force is, the formula itself is still valid
After consulting many books, it is also said that the Coulomb force is effective in the range of R = 10 (- 15th power) m ~ 10 (7th power) M. Why is Coulomb force invalid when it is greater than a certain distance??
It's invalid within 10 (- 15) M. I understand that short distance can't be regarded as point charge, but why can't long distance be regarded as point charge? Beyond the maximum distance, is there no Coulomb force or other formula?
Please don't answer that the distance is too far, the force effect can be ignored, because no matter how small the force is, the formula itself is still valid.

If there is no context, the reference book is completely wrong. As long as the short distance is not zero, the point charge is always true. The formula of Coulomb force has stipulated the point charge, not two charged bodies. As long as the distance between two charged bodies is far enough, it can be regarded as the point charge, so it can be calculated directly (approximately) by Coulomb's law

On August 8, 2008, the Olympic Games were held in Beijing. This day is Friday. What day is August 8, 2010

August 8, 2008 to August 8, 2010 is exactly two years, and the 10 years of 2009 are not leap years, so there are 730 days in two years
730 divided by 7 is equal to 104 more than 2, that is to say, 104 more than two days. So August 8, 2010 is Friday, another two days, that is Sunday

How to make equations for the pursuit problem of mathematics in grade seven?

Generally, there are two velocities in pursuit problem and encounter problem. Let one be x, and the other be expressed by an algebraic formula containing X. according to the known quantity, we can solve the problem by time = distance / sum of two velocities (encounter problem) time = distance / difference of two velocities (pursuit problem)