Question

A student launches a model rocket. The height of the rocket, h, in feet after t seconds is given by the function h =-16t^2 + 16 + 4. Identify the domain of this equation.

Answer 1

The domain of the equation h = -16t^2 + 16t + 4, which represents the height of a model rocket over time, is all non-negative real numbers, as time cannot be negative in this context.

Step-by-step explanation:

In the problem provided, the student is given a quadratic equation to represent the height of a model rocket over time: h = -16t^2 + 16t + 4.

The domain of this equation refers to all the possible values for t (time) that will yield a real number for h (height). Since time can only be positive or zero in this context (you can't launch a rocket in negative time), the domain is all non-negative real numbers.

However, since the rocket can only travel until it hits the ground again, the domain is practically from t = 0 until the time it lands back on the ground.

To find when the rocket hits the ground, we would set h = 0 and solve for t, but the domain remains t ≥ 0 without solving that.