a shark jumps out the water. Yhe function f(x)=-16x^2+21x models the shark's height, in feet, above the water after x seconds. How longis teh shark out of the water
the peak of the jump lies on the axis of symmetry of the parabola
... x = -b / 2a = -21 / (2 * -16)
time up equals time down
time of flight (jump) = 2 * 21/32
To determine how long the shark is out of the water, we need to find the x-values where the height of the shark, given by the function f(x), is equal to zero.
Considering the given function f(x) = -16x^2 + 21x, we set it equal to zero and solve for x:
-16x^2 + 21x = 0
Factoring out x, we have:
x(-16x + 21) = 0
Setting each factor equal to zero individually:
x = 0 (equation 1)
-16x + 21 = 0
Solving the second equation:
-16x = -21
x = -21 / -16
x = 1.3125 (approx.)
Now we have two potential x-values: x = 0 and x ≈ 1.3125.
Since time cannot be negative, we discard x = 0.
Therefore, the shark is out of the water for approximately 1.3125 seconds.