can some one please help me with this question?!

Question

anonymous · Answer

every year in delaware there is a contest where people create cannons and catapults designed to launch pumpkins as far in the air as possible. the equation y=10+95x-16x^2 can be used to represent the height,y, of a launched pumpkin, where x is the time in seconds that the pumpkin has been in the air. What is the maximum height that the pumpkin reaches? How many seconds have passed when the pumpkin hits the ground? 1.The pumpkin's maximum height is 2.97 feet and it hits the ground after 6.04 seconds 
2.The pumpkin's maximum height is 151.02 feet and it hits the ground after 6.04 seconds 3.The pumpkin's maximum height is 2.97 feet and it hits the ground after 151.02 seconds 4.The pumpkin's maximum height is 151.02 feet and it hits the ground after 2.97 seconds

ajspeller · Answer

$$f(x)=10+95x-16x^2$$
$$f(x)=-16x^2+95x+10$$
$$f(x)=Ax^2+Bx+C$$
$$A=-16$$$$B=95$$$$C=10$$
The vertex is the maximum height.

The following expression calculates the time in seconds when the maximum height is reached ...

Seconds
$$ x=\frac{ -B }{ 2A }=\frac{ -95 }{ 2(-16) }=\frac{ -95 }{ -32 }=2.96875 $$
Height
$$y=f(\frac{ -B }{ 2A })=f(2.96875)=-16(2.96875)^2+95(2.96875)+10=151.015625$$

Use the Quadratic Formula to find out when the pumpkin hits the ground

$$x=\frac{ -B \pm \sqrt{B^2-4AC} }{ 2A }=\frac{ -(95) \pm \sqrt{(95)^2-4(-16)(10)} }{ 2(-16) }=\frac{ -95 \pm \sqrt{9025-(-640)} }{ -32 }$$

$$=\frac{ -95 \pm \sqrt{9025+640} }{ -32 }=\frac{ -95 \pm  \sqrt{9665}}{ -32 }=\frac{ -95\pm 98.31073187 }{ -32 }$$

split up into 2 expressions because of the $$  \pm $$ symbol

Disregard the negative value for x, which represents time
$$x=\frac{ -95+ 98.31073187 }{ -32 }=-0.1034603709$$

This positive value for x, which represents time is acceptable.
$$x=\frac{ -95- 98.31073187 }{ -32 }=6.0409603709$$

finallyausername · Answer

did you finish this test? i need help too