To identify the axis of symmetry (AOS) and vertex of the parabola defined by the function f(t) = -16t^2 + 60t + 16, we can follow these steps:
1. AOS (Axis of Symmetry) is given by the formula AOS = -b / (2a), where a is the coefficient of the t^2 term (-16) and b is the coefficient of the t term (60) in the quadratic function.
2. Substitute the values of a and b into the formula:
AOS = -60 / (2*(-16))
AOS = -60 / (-32)
AOS = 1.875
Therefore, the axis of symmetry is t = 1.875.
3. To find the vertex of the parabola, we need to substitute the value of the axis of symmetry (1.875) back into the original function f(t). This will give us the y-coordinate of the vertex.
4. Calculate the vertex by substituting t = 1.875 into the function:
f(1.875) = -16(1.875)^2 + 60(1.875) + 16
f(1.875) = -16*(3.515625) + 112.5 + 16
f(1.875) = -56.25 + 112.5 + 16
f(1.875) = 72.25
Therefore, the vertex of the parabola is (1.875, 72.25).
In conclusion, the axis of symmetry is t = 1.875 and the vertex of the parabola is located at (1.875, 72.25).
