If the image of the square of the function y = x is perpendicular to the tangent of the function image translated by the vector a = (m, 1) at x = 1, then M= nothing

If the image of the square of the function y = x is perpendicular to the tangent of the function image translated by the vector a = (m, 1) at x = 1, then M= nothing

Let f (x) = x ^ 2, f '(x) = 2x, then f' (1) = 2
The image with function y = x ^ 2 is translated by vector a = (m, 1), and the function is g (x) = (x + m) ^ 2 + 1
g’(x)=2(x+m)
G '(1) = 2 (1 + m) = - 1 / 2 = = > m = - 5 / 4
After translation, G (x) = (X-5 / 4) ^ 2 + 1 meets the meaning of the question
∴m=-5/4

What does a function translate by vector mean

Equivalent to the point on the function translating according to the vector, (x, y) translating according to (a, b), then x '= x + A; y'=y+b.

After translating the image of function y = sin2x according to vector a = (π / 4,1), the analytical formula of the function image is

The image of function y = sin2x is translated by vector a = (π / 4, 1)
Is to shift π / 4 to the right
Unit shifts up one unit
Therefore, y = sin2x becomes y = sin (2x - π / 2) + 1 = - cos2x + 1

What does it mean to shift the function image by a vector For example, sin2x translates according to vector a (1, - 2), what do you get? How did you get it? Why do you think so? Please answer carefully

You can think of it this way. The original (0,0) satisfying function is now changed to 1, - 2) satisfying the new function after moving, so there is x '- 1 = XY' + 2 = y instead of Y '+ 2 = sin2 (x' - 1), and then expand it. You can also think of it this way. After moving according to a (1, - 2), the value of X becomes larger, so you need to subtract 1, and if y becomes smaller, you need to add 2 to get y '+ 2 = sin2 (

Similarities and differences of translation, rotation and axisymmetry

This should be an open problem. First of all, let's talk about the differences: the characteristic of translation is that the motion trajectory of each point is the same, and each point on the graph can represent the motion of the whole graph, which is why when studying the translational motion of an object, the object can be abstracted into a physical model - particle. Rotation

Three characteristics of axisymmetric rotation and Translation Hope to have an answer soon! The answer should be marked with serial number or clearly seen! It's a feature!

Translation, rotation and axisymmetry are the three most basic transformations. A figure does not change its shape and size, but changes from one position to another. Translation is to transform a figure from one position to another. In the process of translation, the "forward direction" of each corresponding point remains parallel