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.
Height (feet)
Distance (feet)

Answer 1

Answer:

Option C and option D

Step-by-step explanation:

we have that

$y=x^{2}-4x+5$

This is the equation of a vertical parabola open upward

The vertex is a minimum

Convert the equation into vertex form

Complete the square

$y-5=x^{2}-4x$

$y-5+4=x^{2}-4x+4$

$y-1=x^{2}-4x+4$

$y-1=(x-2)^{2}$

$y=(x-2)^{2}+1$ ----> equation of the parabola in vertex form

The vertex is the point (2,1)

therefore

when the bird is 2 feet away from the first fence post, it reaches its minimum height of 1 foot

Answer 2

Answer: C and D

Step-by-step explanation: