I know that the vertex of the quadratic equation is (-2,144).

My work:

f(t) = -16t^2 - 64t + 80

f(t) = -16(t^2 + 4t) + 80 (I divided the x terms by the leading coefficient and grouped them from the constant.)

f(t) = -16(t^2 + 4t + 2^2) + 80 - 4 (I divided the middle term's coefficient by two and squared it, adding it inside the parentheses and subtracting it outside.)

f(t) = -16(t - 2)^2 + 76 (This is the part I most likely messed up on.)