Question

Flight Path of a Bird

Answer 1

Answer:

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

Step-by-step 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 $y=2(x-2)^2+2$