When the sales season of a shopping mall is approaching, the sales price of a certain brand of children's clothing is on the rise. If the price of this kind of children's clothing is 20 yuan at the beginning, and the price increases by 2 yuan every week (7 days), from the 6th week, keep the stable price of 30 yuan every piece, until the end of the 11th week, the children's clothing will not be sold. (1) please establish the functional relationship between the sales price y (yuan) and week X; (2) If the brand of children's clothing is sold out in the week when it is purchased, and the relationship between the purchase price Z (yuan) of each piece of children's clothing and the week x is Z = - 18 (X-8) 2 + 12, 1 ≤ x ≤ 11, and X is an integer, then after which week does the brand of children's clothing sell out, each piece of children's clothing get the maximum profit? What is the maximum profit?

When the sales season of a shopping mall is approaching, the sales price of a certain brand of children's clothing is on the rise. If the price of this kind of children's clothing is 20 yuan at the beginning, and the price increases by 2 yuan every week (7 days), from the 6th week, keep the stable price of 30 yuan every piece, until the end of the 11th week, the children's clothing will not be sold. (1) please establish the functional relationship between the sales price y (yuan) and week X; (2) If the brand of children's clothing is sold out in the week when it is purchased, and the relationship between the purchase price Z (yuan) of each piece of children's clothing and the week x is Z = - 18 (X-8) 2 + 12, 1 ≤ x ≤ 11, and X is an integer, then after which week does the brand of children's clothing sell out, each piece of children's clothing get the maximum profit? What is the maximum profit?

(1) (2) let the profit be w, and then w = w, then w = w, then w = w = y − z = 20 + 2 (x − 2) (x − 2 (x − 1) + 18 (x − 8) 2 (x − 8) 2-12 = 18x2 + 14 (1 ≤ x ＜ 6) (which is an integer) y − z = 30 + 18 (1 ≤ x ＜ 6) 18 (1 ≤ x ＜ 6) 6 (6) 6) 30 (1 ≤ x ＜ 6) 18 (1 ≤ 6) 30 (1 ≤ 6) 6 (6 ≤ 6) 2 (6 ≤ 6 ≤ 6 ＜ 6) 2 (6 ≤ 6 ≤ 6 ≤ 6 ≤ 6 ＜ 6 ＜ 6 ＜ 6) 2-12 = 18 (x {6) 18 (x \\656565505050508; 258 = 258 + 14 = 258 + 14 = 258 + 18 (X-8) ）When x = 11, Wmax = 18 × 9 + 18 = 1918 = 19.125 (yuan). To sum up, after purchasing and selling in the 11th week, the profit is the largest, which is 19.125 yuan per piece

An applied problem of quadratic function
A store sells a commodity with a purchase price of 20 yuan / piece. If the price is 30 yuan / piece, 100 pieces can be sold every day. If the price is reduced (or increased), the sales volume will increase (or decrease) correspondingly. For every 1 yuan / piece of price reduction (or increase), the daily sales will increase (or decrease) 5 pieces
(1) When the selling price is x yuan / piece, how many pieces is the daily sales volume
(2) Let the daily sales amount be y yuan, and write the functional relationship between Y and selling price X
(3) Color day sales profit is Z yuan, write the functional relationship between Z and price X
Can you give me some ideas?

(1) When the selling price is x yuan / piece, the daily sales volume is: 5 (30-x) - for each price reduction (or price increase) of 1 yuan / piece, the daily sales volume increases (or decreases) by 5 pieces, (30-x) may be positive or negative, and the positive number proves that the price is reduced, and if the price reduction is (30-x) yuan, the sales volume increases by 5 (30-x); if (30-x) is negative, the price is increased by (30-x) yuan, The sales decreased by 5 (30-x) yuan
(2) Y = {100 + 5 (30-x)} × x -------- daily sales = daily sales price × sales volume. If the known daily sales price is x, then the daily sales price obtained from (1) is {100 + 5 (30-x)}. 5 (30-x) is the increase or decrease of daily sales volume
(3) Z = (x-20) × {100 + 5 (30-x)} ---- daily sales profit = (selling price of each garment - purchase price of each garment) × daily sales volume (x-20) is the net income of each garment, {100 + 5 (30-x)} is the daily sales volume,
If you think the explanation is OK, take my answer,

How to do quadratic function problems
A shopping mall sells a batch of famous brand shirts, with an average of 20 pieces sold every day and a profit of 40 yuan per piece. In order to expand sales, the shopping mall decides to take appropriate price reduction measures. According to the investigation, if every shirt is reduced by 1 yuan, the shopping mall can sell 2 more pieces per day on average
1. When the price of each shirt is reduced, the average daily profit of the mall is more than 1200 yuan?
2. If you want to make the most profit every day, how much should you reduce the price of each shirt?

Solution
(1) Suppose the price of each shirt is reduced by X Yuan and the total profit is y yuan
Countable equation
y=(40-x)×(20+2x)
The result is: y = - 2x * x + 60x + 800
∵ from the image, when 10