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?
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. Ask the House
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