Please give a good explanation and show your work as well

A) down

B) x intercept (5, 0)

   y intercept (0, 80)

C) 144 ft

Step-by-step explanation:

y = Ax² + Bx + C

y = -16x² + 64x + 80

A)

Parabola opens down because A is negative

B)

x intercept (5, 0)

x = (-64 ±√(64² - 4(-16)(80))) / (2(-16))

x = -1  which means if the profile is continuous, the balloon launched one hour ago.

or

x = 5 which means the balloon will be on the ground in 5 hours.

(assuming level ground or no wind at all.

y intercept

y = -16(0)² + 64(0) + 80

y = 80 ft

meaning the balloon is already 80 feet above the ground when we start looking at t = 0

C)

Maximum altitude will occur when the vertical velocity is zero. Velocity is the derivative of position.

x' = -32x + 64

0 = -32x + 64

32x = 64

x = 2 hrs

y = -16(2)² + 64(2) + 80

y = 144 ft