A teenager who is 5 feet tall throws an object into the air. The
quadratic function f(x) = - 16x2 + 64x + 5 is where f(x)
is the height of the object in feet and x is the time in seconds.
The function in vertex form is
A f(x) = -16(x -2)^2 - 59
B f(x) = -16(x-2)^2 + 69
C f(x) = -16(x-2)^2 + 5
D f(x) = -16(x-2)^2 - 11
the object hits the ground after about ____ seconds
A 2
B 3
C 4
D 5
C 4
The function in vertex form is f(x) = -16(x -2)^2 + 5
To find when the object hits the ground, we set f(x) = 0 and solve for x:
0 = -16(x - 2)^2 + 5
16(x - 2)^2 = 5
(x - 2)^2 = 5/16
x - 2 = ±√(5/16)
x = 2 ± √(5/16)
x ≈ 2 ± √(5)/4
Since the negative value doesn't make sense in this context, we use the positive value:
x ≈ 2 + √(5)/4 ≈ 4
So, the object hits the ground after about 4 seconds.