Question

1. an airplane drops a beacon over the ocean. the function ( f(x) = -16x^2 + 1600 ) gives the height in feet of the beacon ( x ) seconds after it is dropped. how high is the beacon when it is released? how long does it take the beacon to hit the water?

how high when it is released:

how long to hit the water?:

x	f(x)
1	1584
2	1536
3	1456
4	1344
5	1220
6	1024
7	816
8	576
9	304
10	0

Explanation:

Step1: Find height when released

When the beacon is released, \( x = 0 \). Substitute \( x = 0 \) into \( f(x)=-16x^{2}+1600 \).
\( f(0)=-16(0)^{2}+1600 = 1600 \) feet.

Step2: Find time to hit water

The beacon hits the water when \( f(x)=0 \). Solve \( -16x^{2}+1600 = 0 \).

1. Subtract 1600: \( -16x^{2}=-1600 \)
2. Divide by -16: \( x^{2}=100 \)
3. Take square root: \( x = 10 \) (since time can't be negative).

Answer:

Height when released: 1600 feet; Time to hit water: 10 seconds.