Current location - Training Enrollment Network - Mathematics courses - Summary of knowledge points of mathematical function in junior high school
Summary of knowledge points of mathematical function in junior high school
Function is an important knowledge point in junior high school mathematics. Next, I will summarize the important knowledge points of junior high school mathematical functions and look at the specific content for reference.

Knowledge point of linear function 1. linear function

If y=kx+b(k and b are constants, k≠0), then y is called a linear function of x.

Especially when b=0, the linear function y=kx+b becomes y=kx(k is constant, k≠0), and y is called the proportional function of X.

2. Images and properties of linear functions

Any point P(x, y) on the (1) linear function satisfies the equation: y = kx+b.

(2) The coordinate of the intersection of the linear function and the Y axis is always (0, b), and the coordinate of the intersection of the linear function and the X axis is always (-b/k, 0).

(3) The image of the proportional function always passes through the origin.

(4) The relationship between k, b and the quadrant where the function image is located:

When k>0, y increases with the increase of x; When k < 0, y decreases with the increase of x.

When k>0, b>0, the straight line passes through the first, second and third quadrants;

When k>0, b<0, the straight line passes through the first, third and fourth quadrants;

When k < 0, b>0, a straight line passes through the first, second and fourth quadrants;

When k < 0, b<0, a straight line passes through the second, third and fourth quadrants;

When b=0, the straight line passing through the origin o (0 0,0) represents the image of the proportional function.

At this time, when k>0, the straight line only passes through the first and third quadrants; When k < 0, the straight line only passes through the second and fourth quadrants.

Knowledge point of quadratic function 1. Quadratic function expression

(1) vertex type

y=a(x-h)? +k(a≠0, a, h, k are constants), the vertex coordinates are (h, k), the symmetry axis is a straight line x=h, and the position characteristics of the vertex and the opening direction of the image are related to the function y=ax? When x=h, y = the maximum (minimum) value of k.

(2) Intersection point

y=a(x-x? )(x-x? ) [limited to the parabola intersecting with the x axis, that is, y=0, that is, b? -4ac & gt; 0]

Function and image intersect at (x? 0) and (x? ,0)

(3) general formula

y=aX? +bX+c=0(a≠0)(a, B and C are constants)

2. Symmetry axis of quadratic function

Quadratic function image is an axisymmetric figure. The symmetry axis is a straight line x=-b/2a.

The only intersection of the symmetry axis and the quadratic function image is the vertex p of the quadratic function image.

Especially when b=0, the symmetry axis of the quadratic function image is the Y axis (that is, the straight line x=0).

A and B have the same sign, and the symmetry axis is on the left side of Y axis;

A and B are different symbols, and the symmetry axis is on the right side of the Y axis.

3. Symmetry relation of quadratic function image

(1) For the general formula:

①y=ax2+bx+c and y=ax2-bx+c are symmetric about Y ..

② two images y = ax2+bx+c and y=-ax2-bx-c are symmetrical about X ..

③y=ax2+bx+c and y=-ax2-bx+c-b2/2a are symmetrical about the vertex.

④y=ax2+bx+c and y=-ax2+bx-c are symmetrical about the center of the origin. (i.e., the graph obtained after rotating 180 degrees around the origin)

(2) For vertices:

① two images, y = a (x -h) 2+k and y=a(x+h)2+k, are symmetrical about y axis, that is, vertices (h, k) and (-h, k) are symmetrical about y axis, and the abscissas are opposite, but the ordinate is the same.

② two images, y = a (x-h) 2+k and y=-a(x-h)2-k, are axisymmetrical about x, that is, vertices (h, k) and (h, -k) are axisymmetrical about x, with the same abscissa and opposite ordinate.

③y=a(x-h)2+k and y=-a(x-h)2+k are symmetrical about the vertices, that is, the vertices (h, k) and (h, k) are the same and the opening directions are opposite.

④y=a(x-h)2+k and y=-a(x+h)2-k are symmetrical about the origin, that is, the vertices (h, k) and (-h, -k) are symmetrical about the origin, and the abscissa and ordinate are opposite.