Answer:
See below ↓
Step-by-step explanation:
We need to check the different time intervals to find the max. height
- t = 0 or 1 [both give same result]
- f(1) = -16(1) + 16(1) + 12 = 12 feet
2. t = 2
- f(2) = -16(2)² + 16(2) + 12 = -20 feet
⇒ Clearly as she is diving, her maximum height will be her initial height which is 12 feet
⇒ To achieve this, it takes her 0 seconds [initial height = no time needed]
Taking f(x) = 0 [surface of water → just touching/hit the water]
- 0 = -16x² + 16x + 12
- 4x² - 4x - 3 = 0
- 4x² - 6x + 2x - 3 = 0
- 2x(2x - 3) + 1(2x - 3) = 0
- (2x + 1)(2x - 3) = 0
- x is positive
- x = 3/2 = 1.5 seconds
⇒ After 1 second, she is 12 feet above the water
⇒ The diving board is 12 feet above the water
