Answer:
The airplane reaches its maximum height of 74 feet in 14 seconds.
Step-by-step explanation:
The easiest thing to do here is to plug in the two numbers given in the answer choices. Finding the height at 14 seconds and the height after 74 seconds is straightforward from here.
h (14) = -(14-14)²+ 74
h (14) = 0 + 74
h (14) = 74
h (74) = -(74-14)² + 74
h (74) = -(60)² + 74
h (74) = -3600 + 74
h (74) = -3,526
Now, we know that a height of an airplane won't be negative, as the height below the ground cannot be reached.
because our equation includes -(t-14)², any number greater than 14 will be a larger negative than 0--setting the height to an impossible number.
{However, we add +74 feet, so our t-14 could be any number that is less than 74 when squared (after first subtracting 14 from the number). Numbers like 15, (resulting in subtracting 1 from 74), 16 (resulting in -4 from 74), 17 (74-9), 18 (74-16), 19 (74-25), 20 (74-36), 21 (74-49), 22 (74-64) are still above the minimum input}
{So, our t could be up to 22, and any number above this maximum limit, such as 23, result in a height of 0}
for example: -(23-14)² + 74
-(9)² = -81
-81 + 74 = -7
All numbers below 14, which would end in an eventual negative outcome [ -(x)² = negative if x < 0 ]
are greater than a t of 14.
-(13-14)² = -1
; showing that t = 14 is our maximum height
(remember that if you have -(x)² you get the negative version of x² [pemdas. the negative outside of the parenthesis is equivalent to multiplying the parenthesis by -1. (E)xponents comes before (M)ultiplication].)
so 
