Answer:
A. The maximum heigh is 81 feet
B. The ball will reach the maximum heiight at 2.25 seconds
C. The domain of the function is [tex]t\in [0,4.5][/tex]
D. The range of the function is [tex]h(t)\in [0,81][/tex]
E. 4.5 seconds
Step-by-step explanation:
A ball was thrown into the air with an initial velocity of 72 feet per second. The height of the ball after t seconds is represented by the equation:
[tex]h= -16t^2 + 72t[/tex]
The maximum height will be at parabola's vertex. Find it:
[tex]t_v=\dfrac{-b}{2a}\\ \\t_v=-\dfrac{72}{2\cdot (-16)}=\dfrac{72}{32}=\dfrac{9}{4}=2.25\\ \\h(t_v)=-16\cdot t_v^2+72\cdot t_v\\ \\h(2.25)=-16\cdot 2.25^2+72\cdot 2.25=81[/tex]
A. The maximum heigh is 81 feet
B. The ball will reach the maximum heiight at 2.25 seconds
C. Find where the parabola intersects the x-axis:
[tex]h=0\Rightarrow -16t^2+72t=0\\ \\t(-16t+72)=0\\ \\t_1=0\ \text{or}\ 16t=72,\ t_2=\dfrac{9}{2}=4.5[/tex]
So, the domain of the function is [tex]t\in [0,4.5][/tex]
D. The range of the function is
[tex]h(t)\in [0,81][/tex]
E. The ball is at the air for 4.5 seconds
