Question

A bird takes flight from a branch in a tree. The given function represents the flight of the bird, where f(x) is the height of the bird, in feet, and x is the horizontal distance, in feet, from the start of its flight.
Determine the symmetry of the function.

A.
The flight of the bird is symmetric about the line x = 18 feet, which indicates that the bird is at the same height when it is horizontally 17 feet and 19 feet away from where it began its flight.
B.
The flight of the bird is symmetric about the line x = 4 feet, which indicates that the bird is at the same height when it is horizontally 3 feet and 5 feet from where it began its flight.
C.
The flight of the bird is not symmetric.
D.
The flight of the bird is symmetric about the line x = 2 feet, which indicates that the bird is at the same height when it is horizontally 1 foot and 3 feet away from where it began its flight.

Answer 1

f(x)=1/2x^2-2x+20

h = -b/2a  is the axis of symmetry

h = - (-2)/ (2 * 1/2)

h = 2 /1

the axis of symmetry is  x=2

D.  

The flight of the bird is symmetric about the line x = 2 feet, which indicates that the bird is at the same height when it is horizontally 1 foot and 3 feet away from where it began its flight.