the height of a ball in feet is modeled by \(f(x)= -16x^2 +72x\)where x is the time in seconds after it is hit.
A) How long is the ball in the air?
B) how high does the ball go?
C) When is the ball at a height of 32 feet?
+12530 A) How long is the ball in the air?
B) how high does the ball go?
C) When is the ball at a height of 32 feet?
+37084 A)When the ball hits the ground, the height will be zero so:
0 = -16x^2 +72 x
72= 16x x = 72/16 = 4.5 seconds
B) The ball spends HALF of the time in the air going UP and half of the time coming back DOWN...so it reaches its MAXIMUM at 1/2 x 4.5 = 2.25 Seconds
Hmax = -16(2.25)^2 + 72(2.25) = 81 feet
C) The ball will be at 32 feet TWICE (going UP and coming DOWN)
32 = -16x^2+72x -16x^2 +72x - 32 = 0 Use quadratic formula to find x = 0.5 sec and 4 sec
