Answer:
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
