Question

the function $h(t) = -16t^2 + 28t + 500$ represents the height of a rock $t$ seconds after it is propelled by a slingshot. what does $h(3.2)$ represent? \bigcirc the height of the rock 3.2 seconds before it reaches the ground \bigcirc the time it takes the rock to reach the ground, or 3.2 seconds \bigcirc the time it takes the rock to reach a height of 3.2 meters \bigcirc the height of the rock 3.2 seconds after it is propelled

Explanation:

The function \( h(t) = -16t^2 + 28t + 500 \) is defined as the height of the rock \( t \) seconds after it is propelled. So, when we substitute \( t = 3.2 \) into the function, \( h(3.2) \) represents the height of the rock 3.2 seconds after it is propelled. Let's analyze the other options:

• The first option is incorrect because there's no indication that 3.2 seconds is related to the time before reaching the ground.
• The second option is incorrect because \( h(t) \) gives height, not time to reach the ground (to find time to reach the ground, we set \( h(t)=0 \) and solve for \( t \)).
• The third option is incorrect because \( h(t) \) gives height for a given time \( t \), not time to reach a height of 3.2 meters (to find time to reach 3.2 meters, we set \( h(t) = 3.2 \) and solve for \( t \)).

Answer:

the height of the rock 3.2 seconds after it is propelled