Solution formula of quadratic equation in one variable

The solution of the unary quadratic equation -b+√(b2-4ac)/2a -b-√(b2-4ac)/2a?

The relationship between root and coefficient x1+x2 =-b/ax1* x2 = c/a note: Vieta theorem?

Discriminant?

02

Solid geometric area formula

Straight prism lateral area S=c*h Oblique prism lateral area S=c'*h?

Lateral area of a regular pyramid S = 1/2c * h' lateral area of a regular prism S = 1/2(c+c')h'?

The lateral area of the frustum S = 1/2(c+c')l = pi(R+R)l The surface area of the ball S=4pi*r2?

Lateral area of cylinder S=c*h=2pi*h lateral area of cone S= 1/2*c*l=pi*r*l?

03

Solid geometric volume formula

Volume formula V= 1/3*S*H conic volume formula V= 1/3*pi*r2h?

Oblique prism volume V=S'L Note: where s' is the area of straight section.

Cylinder volume formula V=s*h Cylinder V=pi*r2h?

04

Principles and formulas in geometric proof problems

There is only one straight line between two points. ?

The line segment between two points is the shortest.

The same angle or the complementary angle of the same angle is equal.

05

The same angle or the complementary angle of the same angle is equal.

One and only one straight line is perpendicular to the known straight line.

Of all the line segments connecting the outer point and the point on the line, the vertical line segment is the shortest. ?

06

The axiom of parallelism passes through a point outside a straight line, and one and only one straight line is parallel to this straight line.

If both lines are parallel to the third line, then the two lines are also parallel to each other.

07

The same angle is equal and two straight lines are parallel.

Internal dislocation angles are equal and two straight lines are parallel.

The internal angles on the same side are complementary and the two straight lines are parallel. ?

08

These two straight lines are parallel and the included angle is equal.

Two straight lines are parallel and have equal internal angles.

These two lines are parallel and complementary.

Coordinate characteristics of special points

Coordinate plane points (x, y), transverse to the front and longitudinal to the back;

(+,+), (-,+), (-,-) and (+,-), the four quadrants are divided into front and back;

Y is 0 on the x axis, and x is 0 on the y axis.

Quadrant angle bisector

The bisector of the quadrant angle,

Coordinate features have characteristics,

One, three horizontal and three vertical are equal,

Second, the four horizontal and four vertical directions are just the opposite.

Range of independent variables

The denominator of the fraction is not zero,

Even times can't be negative;

The zeroth radix is not zero,

Algebraic and homogeneous roots can do it.

The condition of the simplest radical

The simplest radical three conditions,

Don't include a denominator in the symbol.

Power finger (number) and root finger (number) should be mutually prime,

The index finger is slightly smaller than the index finger.

A straight line parallel to the axis

A straight line parallel to the axis,

The coordinates of the points are specific,

The straight line is parallel to the X axis, and the ordinate is equal and unequal;

The straight line is parallel to the Y axis, and the abscissa of the point remains unchanged.

Motion law of function image

If an analytic function is written as y=k(x+0)+b and the analytic formula of a quadratic function is written as y=a(x+h)2+k, the following formula can be used:

Translate left and right in brackets,

Finally, translate up and down,

Zuo Zheng's correct responsibility must be borne in mind.

Up and down can't be wrong.

Image formula and properties of linear function

The linear function is a straight line, and the image passes through three quadrants;

The proportional function is simpler, and the straight line passes through the origin;

These two coefficients, k and b, play a great role.

K is the included angle of slope, and b intersects the y axis.

K is right oblique, X increases or decreases and Y increases or decreases;

K is negative to the lower left, and the change law is just the opposite;

The greater the absolute value of k, the farther the straight line is from the horizontal axis.

Image formula and properties of quadratic function

Quadratic parabola, image symmetry is the key;

Openings, vertices and intersections that determine the appearance of the image;

The opening and size are broken by a, and the c axis and the y axis intersect.

The symbol of B is special, and the symbol is associated with A;

First find the vertex position, and use the y axis as the reference line.

The difference between left and right is 0, remember that there is no confusion in your heart;

Vertex coordinates are the most important and appear in the general formula.

The horizontal scale is the axis of symmetry, and the maximum value of the vertical scale function is shown in.

If the position of the symmetry axis is found, the sign is reversed,

Generally, vertices, intersections and different expressions can be interchanged.

Image formula and properties of inverse proportional function

Inverse proportional function has its own characteristics, and hyperbola is far from each other.

K is positive, and the graph is within one or three boundaries.

K is negative, and the graph is within the boundary of 24 (image);

The graph is reduced in the first and third functions, and the two branches are reduced respectively.

In the second and fourth graphs, the two branches are opposite, and the two branches are increased respectively;

The longer the line is, the closer it is to the axis and it will never touch the axis.

Remember the definition of trigonometric function skillfully

The trigonometric functions in junior and middle schools are sine, cosine, tangent and cotangent, which is actually the ratio of the sides of a right triangle. You can use/separate these two words, and then use the following.

Definition of a sentence: An unwise cook taught his apprentice to kill fish and said the following sentence: "Cut the fish phosphorus (neighbor) straight." Positive: sine or tangent, right: opposite positive; Remainder: cosine or cosine, adjacent: adjacent edges indicate that the remainder is adjacent; Tangents are right-angled edges.

Special trigonometric function value memory

First of all, remember that the denominators of sine and cosine values of 30 degrees, 45 degrees and 60 degrees are all 2, and the denominators of tangent and cotangent are all 3. The molecular formula "123,3213927" is enough.

Determination of parallelogram

In order to prove parallelogram, two conditions need to be met. One is that the opposite sides are equal or parallel, and a group of opposite sides can also be equal and parallel. Slant is a treasure. If you divide it equally, you can't run away. It is also useful to have equal diagonal lines. Only "two diagonal lines" can be achieved.

Auxiliary line of trapezoidal problem

Move the trapezoid diagonal, and the two waists will form a line;

Move one waist in parallel, with both waists in the "△" position;

Extend the waist intersection a little, there are parallel lines in the "△";

Make two trapezoidal high lines, and the rectangle will be displayed in front of your eyes;

Know the center line of the waist, don't forget to make the center line.

Add auxiliary line songs

Auxiliary line, how to add it?

Finding the pattern is the key. If there is an angle (horizontal) dividing line in the question, it can be vertical on both sides. The middle perpendicular of the line segment leads to the connecting line at both ends, and the midpoint connecting the two sides of the triangle forms the middle line; A triangle has a midline, and the midline is doubled.

Proportional line segment in a circle

In the case of equal product, change the equal ratio, and find the similarity horizontally and vertically;

Not similar, don't be angry, equal line and equal ratio instead,

Keywords encounter equal ratio, variational equal product, reference projection and circular power,

Parallel lines, scale, and find connecting lines at both ends.

Regular polygon stunt song

To bisect a circle, the value of n must be greater than three.

Connect all the points in turn and connect a regular N polygon in front of your eyes.

Tangent line consists of dividing points, and the tangent line intersects with n points.

When n intersections are vertices, a circumscribed regular N polygon appears.

Regular n polygons are beautiful, with inscribed circles and circumscribed circles.

Both inscribed circle and circumscribed circle are unique, and the two circles are concentric circles.

Its graphic axis is symmetrical, and n axes of symmetry all pass through the center of the circle.

If the value of n is even, central symmetry is convenient.

Vertex and radius are the key points in the calculation of regular N-polygon.

The radius, apome and radius of inscribed circle and circumscribed circle change respectively,

Divided into 2n integers of a right triangle, the calculation is simple.

Oral decision-making in functional learning

The proportional function is a straight line, and the image must pass through the origin.

The symbol of k is the key, which determines the quadrant of the straight line.

Negative k goes through two or four limits, x increases and y decreases,

The up-and-down translation k is a constant, and the linear is obtained by derivation.

Add b up and subtract b down, and the image passes three limits.

Two points determine a line, and the selection coefficient is the key.

The hyperbola of inverse proportional function can be determined by only one point.

Positive k falls within one or three limits, x increases and y decreases,

At any point on the image, the rectangular area remains unchanged.

The symmetry axis is the angular bisector, and the order of x and y can be interchanged.

Quadratic parabola, choose three points,

Judging the positive and negative opening of a, the size of c, y axis,

The sign of △ is the simplest, and the number of intersections on the X axis,

On the left side of the same sign axis of A and B, the parabola translation A remains unchanged.

Vertex guides the image to turn, which can be changed in three forms.

Matching method plays the most important role.