Question

Flight Path of a Bird

In this activity, you'll use quadratic equations to model situations and interpret the solutions to the equation

The flight path of a bird can be represented by this equation, where x represents the horizontal distance, in feet, from a tree

branch and y represents the height, in feet, relative to the ground.

y = 2x2 - 8x + 10

Part A

Question

Rewrite the equation modeling the path of the bird in vertex form by completing the square,

Substitute the values of a, h, and k to complete the equation.

Answer 1

The equation modeling the path of the bird in vertex form is
`y=2(x-2)^2+2`

Explanation:

General vertex form equation:
`f(x) = a(x-h)^2 + k`

where (h,k) is the vertex

The flight path of a bird can be represented by this equation:
`y = 2x^2 - 8x + 10`

To convert the equation in vertex form

Completing the square :

`y = 2(x^2 - 4x + 5)\\y = 2(x^2 - 4x + 5 +(2)^2-(2)^2)\\y = 2(x^2 - 4x + 5 +(2)^2-4)\\y = 2((x-2)^2-4+5)\\y = 2((x-2)^2+1)\\y=2(x-2)^2+2`

Where:

(h,k)=(2,2)

a=2

Hence the equation modeling the path of the bird in vertex form is
`y=2(x-2)^2+2`