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안녕하세요. 제가 캐나다에서 유학생활하고있는데, 지금 어드밴스수학12학년꺼 할께 너무 밀려서요...

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Fencing Gardens, Section 1.1

A gardener has 100 m of fencing with which to enclose two square garden plots. The fences must not have a common side. To form each square fence,she cuts the fencing into two lengths.

 Section 1.1

 

(a) creat a table showing the relationship between the perimeter of one plot and the total area of both square plots.

(b) use information about sequences of differences to determine the relationship between the perimeter of one plot and the total area of both square plots.

(c) determine the relationship between the lengths used to form each fence and the total area of both garden plots if each is formed into a circle instead of a square.

Fencing Gardens section 1.2

In Section 1.1, you investigated and identified the type of relationship between the variable x, the first length of fencing, and the total area A of two square garden plots formed from 100m of fencing

(d) use the data collected in section 1.1 to determine the equation of the curve of best fit, and use the equation to determine the value of x that minimizes the area of each type of garden.

(e) students in the enchanced course also investigated the relationship between the lengths used to form each fence and the total area of both garden plots if each is formed into a circle instead of a square. Use another method to create each equation.

Fencing Gardens Section 1.3

In section 1.2, you created quadratic functions in general form representing the relationships between the variable x, the first length of fencing and the total area A of Two square garden plots formed from 100m of fencing.

(f) create and use the transformational form of each quadratic function to determine the length of x that minimizes the area of the guarden and to show the translation of the basic quadratic function y=x².

In Section 1.2, you also created quadratic functions in general form erpresenting the relationships between the variable x, the first length of fencing, and the total area A or two Circular garden plots formed from 100m of fencing.

(g) create and use the transformational form of each quadratic function to determine the length of x that minimizes the area of the circular gardens and to show the translation of the basic quadratic function y=x²

Fencing Gardens section 1.4

use the general form or the transformational form of each quadratic function you have been examining in sections 1.1 to 1.3 to answer each question.

(h) what are the zeros of each quadratic function?

(i) how can the discriminant of the corresponding quadratic equation be used to find the number of x-intercepts of the graph of each quadratic function, and the nature of the roots of each quadratic equation?

(j) what is the relationship between the coefiicients in each standard form of the function and the sum and products of the roots of corresponding quadratic equation?

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