Question

The function y = x2 – 4x + 7 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, 7)
B. When the bird is 4 feet away from the first fence post, it reaches its minimum height of 7 feet.
C. When the bird is 2 feet away from the first fence post, it reaches its minimum height of 3 feet.
D. Minimum at (2, 3)

Answer 1

From the function y=x^2-4x+7
to complete the square we proceed as follows:
The vertex form is given by:
y=(x-h)^2+k
where (h,k) is the vertex:
thus from the function we shall have:
y=x^2-4x+7
c=(b/2a)²
c=(4/2)²=4
thus adding an subtracting 4 in the expression:
y=x^2-4x+4-4+7
y=(x-2)^2+3
thus the vertex will be:
(2,3)

The answer is:
D. Minimum at (2, 3)

Answer 2

D and C is also the right answer..