Question

Select the point that satisfies

y ≤ x^2 - 4x + 2

A) ( 5,5 )
B) ( 2,2 )
C) ( 4,4 )
D) ( 1,1 )

Answer 1

A) (5, 5)

Explanation:

Put the coordinates of the points to the inequality, and check:

y ≤ x² - 4x + 2

for (5, 5) → x = 5, y = 5

5 ≤ 5² - 4(5) + 2

5 ≤ 25 - 20 + 2

5 ≤ 7 CORRECT :)

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for (2, 2) → x = 2, y = 2

2 ≤ 2² - 4(2) + 2

2 ≤ 4 - 8 + 2

2≤ -2 FALSE

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for (4, 4) → x = 4, y = 4

4 ≤ 4² - 4(4) + 2

4 ≤ 16 - 16 + 2

4 ≤ 2 FALSE

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for (1, 1) → x = 1, y = 1

1 ≤ 1² - 4(1) + 2

1 ≤ 1 - 4 + 2

1 ≤ -1 FALSE

Answer 2

A. (5,5)

Explanation:

1. Plug in (5,5) for the x and y values according to the ordered pair. In this case the equation should turn out like this :5 ≤ 5²- 4(5) + 2

• Simplify the equation : 5 ≤ 25 - 20 + 2
• 5 ≤ 7
• A is the answer because it satisfies the inequality as 5 is less than or equal to seven. Though, in this case it is just less than, but not equal to.