The calculation of quadratic function in the third grade of junior high school The length of a route is measured n times, and N results x1, X2,..., X3 are obtained. If x is used as the approximate value of the length of the route, when x takes what value, (x-x1) m * + (x-x2) * +... + (x-xn) * is the smallest? (* represents the square)

The calculation of quadratic function in the third grade of junior high school The length of a route is measured n times, and N results x1, X2,..., X3 are obtained. If x is used as the approximate value of the length of the route, when x takes what value, (x-x1) m * + (x-x2) * +... + (x-xn) * is the smallest? (* represents the square)

It can be proved that X1 ^ 2 + x2 ^ 2 +... + xn ^ 2 > = (x1 + x2 +... + xn) ^ 2 / N (it can be proved by mathematical induction, which is very troublesome to write, but it is not proved here) so the original formula > = [(x-x1) + (x-x2) +... + (x-xn)] ^ 2 / N = [NX - (x1 + x2 +... + xn)] / N to minimize the original formula

A junior three quadratic function application problem! Master to! Urgent!
A flower garden uses flowerpots to cultivate a certain kind of flower seedlings. Through the experiment, the income of each pot and the number of plants in each pot form a functional relationship. Three plants are planted in each pot, and the average price of a single plant is 3 yuan. Under the same cultivation conditions, with each plant added, the growth will be affected to a certain extent, and the average price of a single plant will be reduced by 0.5 yuan. Write the analytical formula of the modification function, and draw an image (this is calculated). When how many plants are planted in each pot, the income is the largest?

Set the yield as y, and plant x strains in each pot,
y=x[3-(x-3)×0.5]
y=-0.5x²+4.5x （3＜x＜9）
y=-0.5（x-4.5）²+10.125
When x = 4 or x = 5, y = 10
When 4 or 5 plants were planted in each pot, the maximum profit was 10 yuan

Given that the images of quadratic function Y1 = AX2 + BX + C and quadratic function y2 = MX + n intersect at points a (- 2, - 5) and B (1,4), and the intersection of quadratic simple number and Y axis is on the straight line y = 2x + 3, the analytic expressions of the two functions are obtained

The intersection of y = 2x + 3 and Y axis is (0,3), so the intersection of quadratic function and Y axis is (0,3)
Substituting (0,3) a (- 2, - 5) and B (1,4) into quadratic function respectively
c=3
4a-2b+c=-5
a+b+c=4
The solution is a = - 1, B = 2, C = 3
Substituting a (- 2, - 5) and B (1,4) into y2 = MX + N, we get
-2m+n=-5
m+n=4
The solution is m = 3, n = 1
So the analytic expressions of the two functions are
y1= -x^2+2x+3
y2= 3x+1