Respuesta :
Answer:
After 1 second, the marble is 20 feet above the ground
Step-by-step explanation:
Here's how the function f(x) = -16t^2 + 36 represents the situation of dropping a marble from a height of 36 feet:
f(x) represents the height of the marble: The output of the function, f(x), gives you the marble's height above the ground at a specific time.
t represents time: The input of the function, t, represents the time in seconds since the marble was dropped.
-16t^2 represents the effect of gravity: The -16t^2 term shows how gravity accelerates the marble downward. The -16 coefficient is related to the acceleration due to gravity (approximately -32 feet per second squared), adjusted for the units being used.
+36 represents the initial height: The +36 term indicates that the marble was initially dropped from a height of 36 feet.
Key points:
Negative coefficient: The negative sign in front of the 16t^2 term signifies that the marble is falling downward.
Parabolic shape: The function is quadratic, meaning its graph would be a parabola representing the marble's trajectory.
Example:
If you want to find the height of the marble after 1 second, you would plug in t = 1:
f(1) = -16(1)^2 + 36 = 20
This tells you that after 1 second, the marble is 20 feet above the ground.
