Find the domain of the function

The height in feet of a soccer ball that is kicked can be modeled by the function 
​f(t) = -8t² + 24t, where t is the time in seconds after it is kicked.  What is the domain of this function?

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The domain is normally the set of x-values, but in this case it is the set of t-values.  That is the time that the ball is in the air.

Set f(t) equal to zero, and solve for t.  f(t) = 0  represents the ball being in contact with the ground.  When the height of the ball is zero.

-8t² + 24t = 0  {set f(t) equal to zero}
-8t(t - 3) = 0  {factored -8t out}
-8t = 0 or t - 3 = 0  {set each factor equal to zero}
t = 0  or t = 3 {solved each equation for t}

The domain would be the set of values from 0 to 3.
That is the time the ball is in the air after being kicked.

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