A teenager who is 5 feet tall throws an object into the air. The quadratic function f(x) =-16x^2+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 −11
B. f(x)=−16(x−2)^2+69
C. f(x)=−16(x−2)^2−59
D. f(x)=−16(x−2)^2+5
The object hits the ground after about blank seconds.
A. 2
B. 3
C. 4
D. 5
The correct answer is:
B. f(x)=−16(x−2)^2+69
To find the time it takes for the object to hit the ground, set f(x) equal to 0 and solve for x:
0 = -16x^2 + 64x + 5
16x^2 - 64x - 5 = 0
Using the quadratic formula, we get:
x = (64 ± √(64^2 - 4*16*(-5))) / (2*16)
x = (64 ± √(4096 + 320)) / 32
x = (64 ± √4416) / 32
x = (64 ± 66.5) / 32
So, x = (64 + 66.5) / 32 or x = (64 - 66.5) / 32
x = 130.5 / 32 or x = -2.5 / 32
x ≈ 4.08 seconds or x ≈ -0.078 seconds
Since time cannot be negative, the object hits the ground after about 4 seconds. Therefore, the correct answer is:
C. 4