Question

The function y = x^2 – 4x + 5 approximates the height, y, of a bird, and its horizontal distance, x, as it flies from one fence post to another. All distances are in feet. Complete the square to find and interpret the extreme value (vertex). Select two answers: one extreme value and one interpretation.

A. Minimum at (4, 5)
B. Minimum at (2, 1)
C. When the bird is 2 feet away from the first fence post, it reaches its minimum height of 1 foot.
D. When the bird is 4 feet away from the first fence post, it reaches its minimum height of 5 feet.

Answer 1

Answer:

Answer is B and C

Step-by-step explanation:

Answer 2

Answer:

The correct options are : B and C

Step-by-step explanation:

The function which approximates the height y of the bird is given by :

y = x² - 4x + 5

Now, completing the square. we get

⇒ y = x² - 4x + 4 + 1

⇒ y = (x - 2)² + 1

Hence, the minimum value of y occurs when the factor (x - 2)² is minimum

And the minimum value of (x - 2)² is 0

⇒ (x - 2)² = 0

⇒ x - 2 = 0

⇒ x = 2

if x = 2 , then y = 1

So, the minimum occurs at (2 , 1)

Which implies that When the bird is 2 feet away from the first fence post, it reaches its minimum height of 1 foot.

Therefore, The correct options are : B and C