Question

what is a reasonable minimum value for the dependent variable? explain how you arrived at your answer

Answer 1

- The solution steps are given below:

`\begin{gathered} f(x)=-16x^2+64 \\ x\text{ is the time in seconds} \\ f(x)\text{ is the distance of the pumpkin from the ground} \\ \\ \text{ When the pumpkin is on the ground, its distance from the ground is zero. Thus,} \\ f(x)=0,\text{ when the pumpking is on the ground.} \\ \\ -16x^2+64=0 \\ \text{ Subtract 64 from both sides} \\ -16x^2=-64 \\ \text{ Divide both sides by -16} \\ x^2=-(64)/(-16) \\ \\ x^2=4 \\ \text{ Take the square root of both sides} \\ \\ x=\pm√(4) \\ x=+2\text{ or }-2 \\ \\ \text{ Since we cannot have negative time, } \\ x=2\text{ seconds} \end{gathered}`

Final Answer

It takes 2 seconds for the pumpkin to hit the ground