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A toy rocket is launched from the ground straight upward. The height of the rocket above the ground, in feet, is given by the equation h(t)=16t^2 + 64t, where t is the time in seconds. Determine the domain for this function in the given context. Explain your reasoning.

Respuesta :

PhyCS
The rocket cannot penetrate the ground, in a contextual sense, therefore the roots of this equation should be the domain of this function. I'll let you find the roots of this quadratic equation (hint: use the quadratic formula: [tex] \frac{-b\pm\sqrt{b^2-4ac}}{2a} \text{ for the equation } ax^2 + bx + c = 0 [/tex]

Using it's concept, it is found that the domain for the function is the time in which the ball is on the air, given by [tex]t \in [0,4][/tex].

What is the domain of a function?

It is the set that contains all possible values for the function.

In this problem, the function is valid only when the ball is in the air, which is between the roots of the function, hence:

h(t) = 0.

-16t² + 64t = 0.

-16t(t - 4) = 0

Then:

-16t = 0 -> t = 0.

t - 4 = 0 -> t = 4.

The domain for the function is the time in which the ball is on the air, given by [tex]t \in [0,4][/tex].

More can be learned about the domain of a function at https://brainly.com/question/10891721

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