The following graph represents the flight path of a bird after it swooped downward off the roof of a house. The height of the bird off the ground is y, and the number of seconds the bird has been flying is x. The vertex of the flight path of the bird is (3,9) and the height of the roof it flies off is 27 ft. What would be the equation for the flight path of the bird if it were rewritten in vertex form and it was a quadratic function?
(0,25)(3,9)(6,28)
A. y=(2x+3)^2+18
B. y=2(x−3)^2−9
C. y=(x−3)^2+18
D. y=2(x−3)^2+9
E. y=(2x−3)^2+9
The vertex form of a quadratic function is given by y = a(x-h)^2 + k, where (h,k) is the vertex of the parabola.
Given that the vertex is (3,9), we have h = 3 and k = 9.
We also know that the height of the roof is 27 ft, which means that when x = 0, y = 27.
So, we can substitute the values into the equation to solve for 'a':
27 = a(0 - 3)^2 + 9
27 = 9a + 9
18 = 9a
a = 2
Therefore, the equation for the flight path of the bird in vertex form as a quadratic function is:
y = 2(x-3)^2 + 9
Answer: D. y = 2(x-3)^2 + 9.