Advanced MathHardInterpreting a quadratic model's constant
Advanced Math practice question
The height h, in metres, of a ball t seconds after it is hit is modelled by h(t) = −5t² + 12t + 1. Which statement is the best interpretation of the number 1?
- A. The ball was 1 metre above the ground when it was hit.Correct
- B. The ball lands after 1 second.
- C. The ball rises 1 metre after being hit.
- D. The ball's speed was 1 metre per second.
Answer: A. The ball was 1 metre above the ground when it was hit.
h(0) = 1: the height at the moment of the hit.
Why the other answers are wrong
- B. The ball lands after 1 second.
- h(1) = 8, so it has not landed at t = 1.
- C. The ball rises 1 metre after being hit.
- The maximum height is h(1.2) = 8.2, far more than 1 metre above the start.
- D. The ball's speed was 1 metre per second.
- The initial upward speed is 12.
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