Answer:
I and IV
Step-by-step explanation:
Since the height of the basketball reaches above 15 feet, hence the maximum of the function should be greater than 15 feet. Also at 7 seconds, the ball is on the ground, hence f(7) = 0 feet
The maximum of a function is at x = -b/2a
i) f(x) = -(x-3)² + 16 = -(x² - 6x + 9) + 16 = -x² + 6x + 7
The maximum of a function is at x = -b/2a = -6 / 2(-1) = 3
f(3) = -(3-3)² + 16 = 16 > 15
Also f(7) = - (7 - 3)² + 16 = 0
Hence this option is correct
ii) f(x) = -x² + 8x - 7
The maximum of a function is at x = -b/2a = -8 / 2(-1) = 4
f(4) = -4² + 8(4) - 7 = 9 < 15 not correct
Also f(7) = - 7² + 8(7) - 7 = 0
Hence this option is not correct since the maximum f(4) = 9 < 15
iii) f(x) = -(x-3)² + 14 = -(x² - 6x + 9) + 14 = -x² + 6x + 5
The maximum of a function is at x = -b/2a = -6 / 2(-1) = 3
f(3) = -(3-3)² + 14 = 14 < 15
Also f(7) = - (7 - 3)² + 14 = -2
Hence this option is not correct since the maximum f(4) = 9 < 15 and f(7) ≠ 0
iv)f(x) = -x² + 6x + 7
The maximum of a function is at x = -b/2a = -6 / 2(-1) = 3
f(3) = -(3)² + 6(3) + 7 = 16 > 15
Also f(7) = - (7)² + 6(7) + 7 = 0
Hence this option is correct
