Question
3. A rock is thrown from one side of a river to another. The function h(t) = −16t^2 + 35t + 80 gives the height of the rock t seconds after it has been thrown.
1. Find h (2).
A) 95
B) 156
C) 118
D) 86
2. What does h(2) represent in the context of this problem?
A) The height of the rock 2 seconds after it has been thrown.
B) The time it takes for the rock to be 2 inches above the ground.
C) The time it takes for the rock to hit the ground once it has been thrown.
3. Does it make sense to find h (−4) in the context of this problem?
A) Yes, it makes sense because the height could be under sea level.
B) No, it does not make sense because time cannot be negative.
C) No, it does not make sense because we cannot have negative inches.
4. Which of the following parabolas would open downwards?
A) y = −3(x + 4)2 + 9
B) y = (x − 5)2 − 4
C) y = 4(x + 6)2 − 3
D) y = 8(x − 1)2 + 2
1. Find h (2).
A) 95
B) 156
C) 118
D) 86
2. What does h(2) represent in the context of this problem?
A) The height of the rock 2 seconds after it has been thrown.
B) The time it takes for the rock to be 2 inches above the ground.
C) The time it takes for the rock to hit the ground once it has been thrown.
3. Does it make sense to find h (−4) in the context of this problem?
A) Yes, it makes sense because the height could be under sea level.
B) No, it does not make sense because time cannot be negative.
C) No, it does not make sense because we cannot have negative inches.
4. Which of the following parabolas would open downwards?
A) y = −3(x + 4)2 + 9
B) y = (x − 5)2 − 4
C) y = 4(x + 6)2 − 3
D) y = 8(x − 1)2 + 2
Answers
GPT-4o mini
Let's solve the questions one by one.
1. **Find h(2):**
We will plug t = 2 into the function h(t):
\[
h(2) = -16(2)^2 + 35(2) + 80
\]
\[
= -16(4) + 70 + 80
\]
\[
= -64 + 70 + 80
\]
\[
= 6 + 80 = 86
\]
So, **h(2) = 86.**
**Answer:** D) 86
2. **What does h(2) represent in the context of this problem?**
Since h(2) gives the height of the rock 2 seconds after it has been thrown, it represents:
**Answer:** A) The height of the rock 2 seconds after it has been thrown.
3. **Does it make sense to find h(−4) in the context of this problem?**
Since we are measuring time t in seconds after the rock is thrown, negative time does not make sense in this context. Therefore:
**Answer:** B) No, it does not make sense because time cannot be negative.
4. **Which of the following parabolas would open downwards?**
A parabola opens downwards if the coefficient of the squared term is negative. Let's look at each option:
A) \( y = -3(x + 4)^2 + 9 \) (The coefficient is -3, so this opens downwards.)
B) \( y = (x - 5)^2 - 4 \) (The coefficient is 1, so this opens upwards.)
C) \( y = 4(x + 6)^2 - 3 \) (The coefficient is 4, so this opens upwards.)
D) \( y = 8(x - 1)^2 + 2 \) (The coefficient is 8, so this opens upwards.)
Only option A opens downwards.
**Answer:** A) \( y = -3(x + 4)^2 + 9 \)
1. **Find h(2):**
We will plug t = 2 into the function h(t):
\[
h(2) = -16(2)^2 + 35(2) + 80
\]
\[
= -16(4) + 70 + 80
\]
\[
= -64 + 70 + 80
\]
\[
= 6 + 80 = 86
\]
So, **h(2) = 86.**
**Answer:** D) 86
2. **What does h(2) represent in the context of this problem?**
Since h(2) gives the height of the rock 2 seconds after it has been thrown, it represents:
**Answer:** A) The height of the rock 2 seconds after it has been thrown.
3. **Does it make sense to find h(−4) in the context of this problem?**
Since we are measuring time t in seconds after the rock is thrown, negative time does not make sense in this context. Therefore:
**Answer:** B) No, it does not make sense because time cannot be negative.
4. **Which of the following parabolas would open downwards?**
A parabola opens downwards if the coefficient of the squared term is negative. Let's look at each option:
A) \( y = -3(x + 4)^2 + 9 \) (The coefficient is -3, so this opens downwards.)
B) \( y = (x - 5)^2 - 4 \) (The coefficient is 1, so this opens upwards.)
C) \( y = 4(x + 6)^2 - 3 \) (The coefficient is 4, so this opens upwards.)
D) \( y = 8(x - 1)^2 + 2 \) (The coefficient is 8, so this opens upwards.)
Only option A opens downwards.
**Answer:** A) \( y = -3(x + 4)^2 + 9 \)