The problem of primary function and inverse proportional function, the second year of junior high sc

Solution: (1) Because: the straight line passes through the point c(1,5) So: the point c is brought into the straight line to get 5= -k+b to get k=b-5

Bringing k=b-5 into a straight line yields: y= -(b-5)x+b= (5-b)x+b Bringing the point (a,0) into a straight line yields:

0= (5-b)*a +b So a= =>apoint coordinates: a( ,0).

Because a= so b= substitute (a,0) into y= -kx+b => k=

2) The abscissa of point d is 9, so we get y==, so d(9, ) substitutes point d into the linear equation.

9k+b => b= , because a= , so a=10, k= b-5=

The equation for the straight line is y= - x+, and the abscissa of the intersection of the line and the x-axis a is 0= - x+ and x=10

The triangle coa is based on OA, and the ordinate of c is high, so we can know that scoa = * bottom * height = *10 * 5 = 25

The area of the triangle COA is 25

Wow, it's been a long time! Solution: The coordinates of point A are [<5+k> k,0]! The relation is ak=5+k, and then the area of the second question is 5*10*! It's been a long time....

1 Substituting (1,5) into y=-kx+b to get 5=-k+b, because point a is (a,0) and substituting b=a, so a=5+k

2. Substitute the two points of cd into the equation to solve y=-5 9x+40 9, which can be calculated by yourself, point c is the height of the x-axis, a=8, and then use the formula of the triangle.

Primary function: Let y=kx+b from the meaning of the question: the coordinates of the point b are (0,-2) and bring (0,-2)(2,0) into the above equation to obtain :

b=-22k+b=0 gives b=-2, k=1, so the analytic formula of the primary function is y=x-2

I dare not guarantee that it is right, it is purely an assumption, and there is a high possibility of being wrong. Inverse proportional function:

The crossing point c is a perpendicular parallel to the y-axis, the perpendicular line parallel to the x-axis intersects the point e so that de is perpendicular to ce, and the perpendicular line of the point c intersects the x-axis at the point f

From the title, it can be seen that ac:cd=2:6=1:3

So af=2, then the coordinates of the point c are (4, double the root number two) [It feels outrageous, don't write it down, shame.] See if you have any ideas].

Inverse proportional function expression: y=3 x

Primary function expression: y=x-2

Since oa=ob,a(2,0) so b coordinates (0,-2), so the primary function is y=x-2

After C is the vertical x-axis of CF, so the angle CAF is 45 degrees, because OA=AC, so AC=2, so CF=AF=root number 2, so C(2+root number2, root number2) brings in the inverse proportional function expression, y=(2 times the root number, 2+2) x

oa=ob, so the coordinates of point b (0,2), so the primary function is x-y-2=0, oa=ac, the slope of the straight line is known, you can find the coordinates of point c (root number 2+2, root number 2), so y = (2+2 times the root number 2) x

oa=ob, the slope of the straight line is 1, oab=45 degrees of the straight line equation is easy to find, is y=x-2

And OC=OA, so the coordinates of point C are (2 + root number 2, root number 2), and there is a point to find the hyperbolic equation, which is.

xy = (2 + root number 2) multiplied by root number 2

1.OAB translates 6 3 units to the right, and the coordinates of each point of the shape are translated 6 3, that is, the ordinate is unchanged, and the abscissa is 6 3 units, then the point A'(3√3，3)

If the point a falls exactly on the inverse proportional function y=k x, then the horizontal and vertical coordinates in the point a satisfy the inverse proportional function, and the horizontal and vertical coordinates of the point a are substituted to obtain k=9 3

9√3/x2.According to the formula of the distance between two points, ob=6=oa

Rotate the OAB in a counterclockwise direction, i.e., its trajectory is "a circle with O as the center of the circle r=6 as the radius", then the equation is: x 2

y 236 can find the intersection point of the garden and the inverse proportional function.

Solution: x1 = 3

x2=-√3

x3=3√3 x4=

y1=9y2=-9 y3=

3 y4=-3

Because the angle of rotation is less than 90°, the two intersections must be located in the third quadrant, that is, the horizontal and vertical coordinates are both negative, and a can be obtained'(-√3,-9),b

After rotation, point A to A', so the angle of rotation.

aoa'Connect AA', oa', to get the new oaa', which can be obtained by the formula for the distance between two points: oa

oa'=aa

6 so oaa'

aa'o∠a'oa

Rotation angle a = 60°

1. Move to the right.

6 3 units, the coordinates of a are (3 3, 3), and bringing the coordinates into the analytic formula gives k = 9 3 , so y = 9 3 x

The trajectory of point 2,,a is a circle, the equation is x 2 + y 2 = 36, the intersection of this circle and y = 9 3 x is c(-3 3,-3), d(-3,-3 3).

The triangle formed by these two points and the triangle OAB are congruent, so it is possible to calculate a=60°

For example, the inverse proportional function y=k x

Note that his image is hyperbola.

When k>0

time in one or three quadrants.

When k<0 is in the second quadrant.

Quadratic function y=ax 2+bx+c

It is common to pay attention to the opening direction of the parabola at a>0 or <0, and then discriminate the intersection of the x-axis with a formula greater than less than 0. There is also the issue of the axis of symmetry, taking the maximum value and the minimum value of x, and so on. It's better to find a few typical questions to do and summarize them.

The analytic formula of the inverse proportional function is obtained from the coordinates of the p point, y=-2 x, and the q point is on the inverse proportional function image, so m=-2, and the analytical formula of the function can be obtained from the coordinates of the p,q highlight as y=-x-1

Draw the picture yourself.

1. Let the inverse proportional function be y=k x because p(-2,1) is on the inverse proportional function, so bring in 1=k -2 so k=-2 i.e. the inverse proportional function is y=-2 k, and because q(1,m) is on the inverse proportional function, so m= -2 1 = -2 q(1,-2) p,q is on a primary function, and bring the coordinate point into y=kx+b, and finally get y= -x-1

2. Draw a line to draw a dot The inverse proportion is a hyperbola, a function, find two points, and connect a straight line.

The primary function y of the independent variables k and x has the following relationship: y=kx+b (k is an arbitrary non-zero constant, b is an arbitrary constant) When x takes a value, y has and only one value corresponding to x. If there are two or more values corresponding to x, it is not a one-time function.

x is the independent variable, y is the value of the function, k is the constant, and y is the primary function of x. In particular, when b = 0, y is a proportional function of x. Namely:

y=kx (k is constant, but k≠0) proportional function image passes through the origin.

y=kx=b.

When k is 0, y increases as x increases.

When k is 0, y decreases as x increases.

The general formula y=ax 2 (superscript) + bx + c (a≠0, a, b, c are constants), and the vertex coordinates are (-b 2a, (4ac-b 2 4a) ;

Vertex formula y=a(x+h) 2+k(a≠0, a, m, k are constants) or y=a(x-h) 2+k (a≠0, a, h, k are constants), vertex coordinates are (-h,k) or (h,k) axes of symmetry are x=-h or x=h, the position features of vertices and the opening direction of the image are the same as those of the function y ax;

Intersection y=a(x-x1)(x-x2) [limited to parabolas with intersection points a(x1,0) and b(x2,0) with x-axis i.e., y=0]; Important concepts: a, b, c are constants, a≠0, and a determines the opening direction of the function. a>0, the opening direction is upward; a<0, the opening direction is downward.

The absolute value of a determines the size of the opening. The larger the absolute value of a, the smaller the opening, and the smaller the absolute value of a, the larger the opening.

Newton's interpolation formula (known as the analytical formula of the three-point function).

y=(y3(x-x1)(x-x2))/((x3-x1)(x3-x2)+(y2(x-x1)(x-x3))/((x2-x1)(x2-x3)+(y1(x-x2)(x-x3))/((x1-x2)(x1-x3) 。From this, the coefficient a=y1 (x1*x2) (y1 is the intercept) of the intersection formula can be derived.

To the right of a quadratic function expression is usually a quadratic trinomial.

Find the root formula. x is the independent variable and y is the quadratic function of x x1,x2=[-b ( b 2-4ac)))] 2a (i.e., the formula for finding the root of a quadratic equation) (as shown in the figure on the right) There are also methods for finding the root by factorization and matching methods The case of the intersection of the quadratic function with the x-axis When b 2-4ac>0, the function image has two intersections with the x-axis. When b 2-4ac=0, the function image has an intersection with the x-axis. When b 2-4ac<0, the function image has no intersection with the x-axis.