Question

The function y = x 2 – 4x + 8 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

Answer 1

Answer: minimum at( 2,4)

Explanation:

A p e x

Answer 2

Exterme Value:
`(2,4)`.

The bird reaches its minimum height which is 4ft affter covering a horizontal distance of 2 ft.

Explanation:

The given function is
`y=x^2-4x+8`.

We add and subtract the square of half the coefficient of x.

`y=x^2-4x+(-2)^2-(-2)^2+8`.

The first three terms form a perfect quadratic trinomial.

`y=(x-2)^2+4`.

This function is now written in the form
`y=a(x-h)^2+k`, where (h,k) is the extreme value(vertex).

The extreme value or the vertex is
`(2,4)`.

Interpretation:

The bird reaches its minimum height which is 4ft affter covering a horizontal distance of 2 ft.