Given that f(x)=x^2 . in the space below, type a function that would shift f(x) right 2.5 units, down 7 units, vertically shrink the function by a factor of 2/5, and reflect is across the x-axis?

Translation by h right and k up: f(x-h)+k.
Vertically scale by k and reflect across the x-axis: -k·f(x).

After the translation, your function is
  f(x) = (x-2.5)² -7

After the scaling and reflection, your function is
  f(x) = (-2/5)((x -2.5)² -7)