Select the point that satisfies the equation

option C

(4,4)

Step-by-step explanation:

Given in the question an inequality

y ≤ x² - 3x + 2

(1,1)

when x = 1

y ≤ 1² - 3 + 2

y ≤ 0

1 ≤ 0

Rejected as 1 is greater than 0

(2,2)

when x = 2

y ≤ 2² - 3(2) + 2

y ≤ 0

2 ≤ 0

Rejected as 2 is grater than 0

(4,4)

when x = 4

y ≤ 4² - 3(4) + 2

y ≤ 6

4 ≤ 6

Accepted as 4 is lesser than 6

(3,3)

when x = 3

y ≤ 3² - 3(3) + 2

y ≤ 2

3 ≤ 2

Rejected as 3 is greater than 2

The correct answer is option A (5, 5)

Step-by-step explanation:

From the figure we can see an equation

y ≤ x² - 4x + 2

Check option A (5, 5)

Substitute the value of x and y in equation

y ≤ x² - 4x + 2

5 ≤ 5² - (4 * 5) + 2

5 ≤ 25 - 20 + 2

5 ≤ 27 - 20

5 ≤ 7

It is true. Therefore the first option is the correct answer