For this case we have the following function that models the problem is:
![y = 10 + 95x-16x ^ 2 ](/tpl/images/0274/1007/d2962.png)
The time for which the maximum height occurs is obtained by deriving the equation:
![y '= 95-32x ](/tpl/images/0274/1007/25424.png)
We equal zero and clear x:
![95-32x = 0 32x = 95 x = 95/32 x = 2.97 ](/tpl/images/0274/1007/cb7be.png)
The maximum height is obtained by evaluating the time obtained in the given equation:
![y = 10 + 95 * (2.97) -16 * (2.97) ^ 2 y = 151.02](/tpl/images/0274/1007/aac0b.png)
Then, by the time it reaches the ground we have:
![10 + 95x-16x ^ 2 = 0 ](/tpl/images/0274/1007/ffcfc.png)
From here, we clear x solving the quadratic equation:
![x = \frac{-95+/- \sqrt{95^2-4(-16)(10)} }{2(-16)}](/tpl/images/0274/1007/ce712.png)
We discard the negative root, and obtain as a result:
2.The pumpkin's maximum height is 151.02 feet and it hits the ground after 6.04 seconds