Respuesta :
Answer:
h(t) = -3(t-8)(t+4). and 8 minutes
Step-by-step explanation:
The function can be written as: h(t) = - 3(t² - 4t - 32). As per quadratic equation, after take off, the drone will land on the ground after 8 minutes.
What is a quadratic equation?
A quadratic equation is an equation that contains a variable with highest degree of 2.
Given, the height of the drone t minutes after take off is modeled by
h(t) = - 3t² + 12t + 96 = - 3(t² - 4t - 32)
Therefore, the function can be written as: h(t) = - 3(t² - 4t - 32)
Therefore, we can write the equation as:
t² - 4t - 32 = 0
⇒ t²- 8t + 4t - 32 = 0
⇒ t(t - 8) + 4(t - 8) = 0
⇒ (t + 4)(t - 8) = 0
Hence, (t + 4) = 0 and (t - 8) = 0
Therefore, t = -4, 8.
As 't' can't be negative, therefore, t = 8.
Therefore, after take off, the drone will land on the ground after 8 minutes.
Learn more about a quadratic equation here: https://brainly.com/question/11872809
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