How to find the axis of symmetry? How do you find the axis of symmetry?

For example, to find the symmetry axis of a sinusoidal function, because the function value of the symmetry axis is the maximum, you can let f(x) be the maximum, and then find the corresponding x. Because the sinusoidal function is a periodic function, there are an infinite number of axes of symmetry on r.

The function value of the center of symmetry is 0, and the method is as above.

For the quadratic function, the axis of symmetry y=ax 2+bx+c is x=-b 2a

Summary. Hello, glad to answer for you. The axis of symmetry is found like this:

f(x) satisfies f(a+x)=f(a-x), then x=a is the axis of symmetry. f(x) satisfies f(a+x)=f(b-x), then x=(a+b) 2 is the axis of symmetry. The parabola is a quadratic function, in the plane Cartesian coordinate system, find the vertices of the quadratic function, and do perpendicular to the x-axis, which is the symmetry axis of the quadratic function (parabola), if you want the formula:

x=-b/2a。

Hello, glad to answer for you. The axis of symmetry is so implicit: f(x) satisfies f(a+x)=f(a-x), then x=a is the axis of symmetry.

f(x) satisfies f(a+x)=f(b-x), then x=(a+b) 2 is the axis of symmetry. The parabola is a quadratic function, in the plane straight with the angle of call coordinate system, find the vertex of the quadratic function, to the x-axis perpendicular, this is the quadratic function (parabola) axis of symmetry, if you want the beam annihilation formula: x=-b 2a.

Axis of Symmetry: Makes the geometry form a straight line that is axisymmetric or rotationally symmetrical. When one part of a symmetrical figure rotates around it at a certain angle, it coincides with the other part.

Many graphs have axes of symmetry. For example, ellipses and hyperbolas have two axes of symmetry, and parabola has one. The axis of symmetry of a regular cone or cylinder is a straight line through the center of the base circle to the vertex or the center of another base circle.

First, the concept of symmetry of points on straight lines is introduced: if points A and B are on both sides of a straight line, and they are the perpendicular bisector of line segment AB, then points A and B are called symmetrical points with respect to straight lines, points A and B are called symmetry points with respect to straight lines, and straight lines are called symmetry axes. On a plane, if all the points of the graph f are axially symmetrical with respect to the straight lines on the plane, the straight lines are called the axes of symmetry under the graph.

On a plane, if there is a straight line, the graph is composed of all the points of the graph f with respect to the symmetry points of the line. If it is still the figure f itself, the figure f is called an axisymmetric figure, and the file has been changed to one of the symmetry axes of the straight line.

The axis of symmetry of y=sinx x=k + 2 centers of symmetry (k,0).

Y=axis of symmetry of cosx x=k center of symmetry (k + 2,0).

Axis of Symmetry: When one part of the graph rotates around it at a certain angle, it coincides with the other. Many graphs have axes of symmetry. For example, an ellipse, a hyperbola has two axes of symmetry, and a parabola has one.

A positive conic or cylinder is a straight line over the center of the base circle and the vertex or the center of another base circle.

Applications

In natural science and mathematics, symmetry means the invariance under a certain transformation, that is, "the invariance of the configuration of the component under the action of its self-isomorphic transformation group", and the usual forms include mirror symmetry (left and right symmetry or bilateral symmetry), translational symmetry, rotational symmetry and telescopic symmetry.

In physics, conservation laws are associated with some kind of symmetry. In everyday life and in Qi Lead's artworks, "symmetry" has more meanings, often representing a certain sense of balance and harmony, which in turn is associated with grace and solemnity.

Algorithm of the axis of symmetry: for the quadratic function y=ax +bx+c, the axis of symmetry is the straight line x=-b 2a, and because y=-x +3ax-2, the axis of symmetry is x=(-3a) (2)=3a 2.

Solution process: y=-x +3ax-2=-(x -3ax)-2=-(x -3ax+9 4a)+9 4a -2=-(x-3 2a) +9 4a -2. The symmetry axis of a quadratic function refers to the linear line where the independent variable x is located when the quadratic function has a maximum.

This straight line is called the axis of symmetry of the function.

Extended Late Lease Materials:

The steps to find the axis of symmetry are as follows:

y=ax^2+bx+c (a≠0)

1. When 0, x 1+x 2= -b a x 1=x 2, and the axis of symmetry x=-b 2a.

2. When <0, a>0 y>0, a<0 y<0, y≠0, ax 2+bx+c-y=0 0, so the axis of symmetry x=-b 2a.

y becomes the opposite number, x does not change, then y=a(-x) 2+b(-x)+c, that is, y=ax 2-bx+c.

When you bring all the values into the image, you find a line that bisects them symmetrically, and that line is the axis of symmetry of the function.

Symmetry axis method of letter dismantling celery silver number:

y=ax^2；+bx+c（a≠0）。

When 0:

x 1+x 2=-b first ax 1=x 2.

axis of symmetry x=-b 2a.

When 0:y> the banquet 0,a

Algorithm for the axis of symmetry: for the quadratic function y=ax +bx+c, the axis of symmetry is the straight line x=-b 2a, and since y=-x +3ax-2, the axis of symmetry is x=(-3a) (-2)=3a 2.

Solution process: y=-x +3ax-2=-(x -3ax)-2=-(x -3ax+9 4a)+9 4a -2=-(x-3 2a) +9 4a -2. The symmetry axis of the quadratic function refers to the straight line where the independent variable x is located when the quadratic function has a maximum.

This straight line is called the axis of symmetry of the function.

1. Formula method: the axis of symmetry of y=ax +bx++c is: y=-b 2a

2. Matching method: Formulate the expression of the quadratic function in the form of y=a(x-h) +k, and the axis of symmetry is: x=h

There is a formula for the axis of symmetry, -b 2a, and according to the increase interval of the problem, we can find the range of values, mathematics is to memorize formulas, set formulas.

For the quadratic function y=ax +bx+c, its axis of symmetry is the straight line x=-b 2a.

Here is y=-x +3ax-2, and the axis of symmetry is naturally x=(-3a) (-2)=3a 2.

The meaning of the axis of symmetry is the value of x between the two points of x1 and x2 when y is equal, that is, the axis of symmetry x=(x1+x2) 2.

When y is equal, ax1 2+bx1+c=ax2 2+bx2+c=> ax1 2+bx1=ax2 2+bx2=> ax1 2-ax2 2=-(bx1-bx2)=> a(x1 2-x2 2)=-b(x1-x2)=> a(x1+x2)(x1-x2)=-b(x1-x2)=> a(x1+x2)=-b

x1+x2=-b/a

Since the axis of symmetry x=(x1+x2) 2 and x1+x2=-b a, the axis of symmetry x=-b a2

In y=asin(wx+a), its symmetry axis can be found in such a way that wx+a=vultures 2+kv, k z, and x. If the axis of symmetry is known, then directly let wx+a=axis of symmetry.

The formula for the axis of symmetry is b -2a The quadratic coefficient in a quadratic equation is a and the primary coefficient is b