Question

Задача достаточно сложная , нужно полное решение с объяснением. Даю за эту задачу максимальное кол-во баллов .

Answer 1

Ответ:

$y=frac{11}{8}|x| - frac{3}{8}|x-8|-x-1$

Объяснение:

$y=a|x|+b|x-8|+kx+c$

точки

(-2;0)

(0;-4)

(8;2)

(9;2)

$begin{cases}2a + 10b - 2k + c = 0\8b + c = -4\8a + 8k + c = 2\9a + b + 9k + c = 2end{cases}$

$begin{cases}2a + 10b - 2k + c = 0\c = -8b-4\8a + 8k + c = 2\9a + b + 9k + c = 2end{cases}$

$begin{cases}2a + 10b - 2k -8b-4 = 0\c = -8b-4\8a + 8k -8b-4 = 2\9a + b + 9k -8b-4 = 2end{cases}$

$begin{cases}2a + 2b - 2k - 4 = 0\c = -8b-4\8a + 8k -8b = 2+4\9a - 7b + 9k - 4 = 2end{cases}$

$begin{cases}2a + 2b - 2k - 4 = 0 /:2\c = -8b-4\8a + 8k -8b = 6 /:2\9a - 7b + 9k = 2+4end{cases}$

$begin{cases}a + b - k - 2 = 0\c = -8b-4\4a + 4k -4b = 3\9a - 7b + 9k = 6end{cases}$

$begin{cases}a =-b+k+2\c = -8b-4\4a + 4k -4b = 3\9a - 7b + 9k = 6end{cases}$

$begin{cases}a =-b+k+2\c = -8b-4\4(-b+k+2) + 4k -4b = 3\9(-b+k+2) - 7b + 9k = 6end{cases}$

$begin{cases}a =-b+k+2\c = -8b-4\-4b+4k+8 + 4k -4b = 3\-9b+9k+18 - 7b + 9k = 6end{cases}$

$begin{cases}a =-b+k+2\c = -8b-4\- 8b + 8k + 8 = 3\- 16b + 18k + 18 = 6 /:2end{cases}$

$begin{cases}a =-b+k+2\c = -8b-4\- 8b + 8k + 8 = 3\-8b+9k +9 = 3end{cases}$

$begin{cases}a =-b+k+2\c = -8b-4\- 8b = 3-8k-8\-8b+9k = 3-9end{cases}$

$begin{cases}a =-b+k+2\c = -8b-4\- 8b = -8k-5\-8b+9k =-6end{cases}$

$begin{cases}a =-b+k+2\c = -8b-4\- 8b = -8k-5\-8k-5+9k = -6end{cases}$

$begin{cases}a =-b+k+2\c = -8b-4\- 8b = -8k-5\k = -6+5end{cases}$

$begin{cases}a =-b+k+2\c = -8b-4\- 8b = -8k-5\k = -1end{cases}$

$begin{cases}a =-b-1+2\c = -8b-4\- 8b = -8 cdot (-1)-5\k = -1end{cases}$

$begin{cases}a =-b+1\c = -8b-4\- 8b = 8-5\k = -1end{cases}$

$begin{cases}a =-b+1\c = -8b-4\- 8b = 3 /:(-8)\k = -1end{cases}$

$begin{cases}a =-b+1\c = -8b-4\b = - frac{3}{8} \k = -1end{cases}$

$begin{cases}a =-left(- frac{3}{8} right) +1\c = -8 cdot left( - frac{3}{8} right) -4\b = - frac{3}{8} \k = -1end{cases}$

$begin{cases}a = frac{3}{8} +1\c =3 -4\b = - frac{3}{8} \k = -1end{cases}$

$begin{cases}a = frac{11}{8}\c = -1\b = - frac{3}{8} \k = -1end{cases}$