One way is to use PlotStyle and PlotLabel:
Animate[Plot[{x^2 - 1, x^2, -1/(2 a) (x - a) + a^2}, {x, -3, 3},
PlotRange -> {{-3, 3}, {-2, 9}}, Axes -> {True},
AspectRatio -> Automatic, PlotStyle -> {Black, Blue, Red},
PlotLabel -> Row[{"a = ", a}]], {a, -1, 1}, RefreshRate -> 60,
AnimationDirection -> ForwardBackward, DefaultDuration -> 4]