To find the vertex form of the quadratic function representing the flight path of the bird, we can use the vertex form of a quadratic function: y = a(x-h)^2 + k, where (h,k) is the vertex.
Given that the vertex is (3,9), the equation would be:
y = a(x-3)^2 + 9
Since the height of the roof the bird flies off is 27 ft, this gives us a point on the flight path (0,27). We can then substitute this point into the equation:
27 = a(0-3)^2 + 9
27 = 9a
a = 3
Therefore, the equation in vertex form would be:
y = 3(x-3)^2 + 9
y = 3(x^2 - 6x + 9) + 9
y = 3x^2 - 18x + 27 + 9
y = 3x^2 - 18x + 36
So, the equation for the flight path of the bird in vertex form, as a quadratic function, is:
y = 3x^2 - 18x + 36
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?
(1 point)
Responses
y=(2x−3)2+9
y=(2x+3)2+18
y=2(x−3)2−9
y=2(x−3)2+9
y=(x−3)2+18
1 answer