The guardrail of a company s lawn is made up of 50 parabolas of the same shape Answer

The key to this problem is to establish a planar Cartesian coordinate system

Solution: (1) Take the point 0 as the origin, the straight 0a as the horizontal axis, and the direction of ray 0a as the positive direction of the x-axis. The straight line perpendicular to the point o and 0a establishes a planar Cartesian coordinate system for the y-axis.

Let this parabolic analytic formula be y= (a≠0).

As can be seen from the title, the coordinates of the parabolic vertices are (1,.

The analytic formula for the parabola of a=is y=-

2) When x=, y=-

When x=, y=-

When x=, y=-

When x=1 6, y=-

The total length of the steel pipe required is 50 2 (

Analysis: According to the characteristics of the built coordinate system, the analytical formula can be set to the form of y=ax2c, combined with the image to easily find the coordinates of point b and point c, and the analytical formula can be substituted to solve the system of equations to obtain the value of the analytical formula of a and c.

Find b3 according to the symmetry

B4 and then find the total length Answer: Solution: From the meaning of the question, b(0,,0) let the analytic formula of the parabola be: y=ax2

c，a+c＝0c＝

Substitution: A 12

c 12 so the analytic formula is: y=-12

x2+12 when x=, y=, when x=, y=, b1c1b2c2b3c3b4

c42 (m), the total length of the required stainless steel pipe is: m) Comments: This question examines the application of quadratic functions, mathematical modeling ideas are the conventional means to use mathematical knowledge to solve practical problems, and it is important to establish an appropriate coordinate system

Establish a planar Cartesian coordinate system, for example: build the origin at the highest point of the parabola, build the y-axis in the symmetrical place, let y=ax 2, and find a=, so l=[(

Choose c :(1) from the title to get b(0,,0).

Let the analytic formula of the parabola be: y=ax2+c

Substituting yields a=-12c=12

The analytic formula is: y=-12x2+12

2) When x=, y=-

When x=, y=-

B1C1+B2C2+B3C3+B4C4=2 (m The total length of the required stainless steel pipe is: m

Solution: (1) b(0,,0) from the meaning of the question

Let the analytic formula of the parabola be: y=ax2+c

The analytic formula for substitution is:

2) When x=, y=-

When x=, y=-

B1C1+B2C2+B3C3+B4C4=2 (m The total length of the required stainless steel pipe is: m

Therefore, C 160m

8.The fence of a park lawn is composed of 100 parabolas of the same shape In order to be firm, each section of the fence needs to be spaced to add a stainless steel pillar, and the highest point of the fence is separated from the bottom as shown in the figure), then the length of the stainless steel pillar ab of this fence is ( ).

Is it this question, if it is option A

Establish a Cartesian coordinate system, and the parabolic vertices are located on the y-axis, then the vertex coordinates (0 , so you can set the parabolic function expression y=ax 2+

Then since the coordinates (1,0) are on the parabola, the substitution yields a=, so that the parabolic function expression is y=.

When x=, y=-When x=, y=-

The total length is 100*2*(

c Analysis: According to the built BAI

The characteristics of the coordinate system can be set to the form of y=ax2 +c, and the combination of the diagram is easy to find point b and point c.

2) When x=, y=-

When x=, y=-

B1C1+B2C2+B3C3+B4C4=2 (m The total length of the required stainless steel pipe is: m

Therefore, c

Solution: (1) b(0,,0) from the subject code ant limb

Let the analytic formula of the parabola be: y=ax2+c

Substitution yields a=-

c=, so the analytic formula is: y=-

x2+2) when x=, y=, when x=, object disturbance y=, b1c1+b2c2+b3c3+b4c4=2 (m.

The total length of the stainless steel pipe required for the later generations is: meters

（1）c（1，0）

Let the analytic formula of the parabola be: y=ax2+c

The analytic formula is: y square plus.

2）x-11

y00(3)-1 is less than or equal to x less than or equal to 1

4) When x=, y=, when x=, y=, b1c1+b2c2+b3c3+b4c4=2 (m The total length of the stainless steel pipe required is: m

Solution: Establish a Cartesian coordinate system as shown in the figure, then the coordinates of point A are (-1,0), the coordinates of point B are ((1,0), the coordinates of point C are (0,,The coordinates of point D are (,0), and the coordinates of point F are (,0), let the parabolic analytical formula be y=a(x-1)(x+1), and substitute c(0, into a=, so the parabolic analytic formula is y=, when x=, y=, when x=, y=, so de=, fp=, so each section of guardrail needs the length of stainless steel pillars = 2 (de+fp)=2 (, so the total length of the stainless steel pillar is required for the 100-section guardrail=100, so c

The key to this problem is to establish a plane Cartesian coordinate system Solution: (1) Take point 0 as the origin, straight practice 0a as the horizontal axis, and take the direction of ray 0a as the positive direction of the x-axis. The straight line perpendicular to the point o and 0a establishes a planar Cartesian coordinate system for the y-axis (as shown in 26-3-i3).

Let this parabolic analytic formula be y=

a≠0) can be seen from the title, the orange companion of the parabolic vertex sitting cavity is (1,.

The solution of a=- is y=-

2) When x=, y=-

When Wu Yan x=, y=-

When x=, y=-

When x=1 6, y=-

The total length of the steel pipe required is 50 2 (