The graph of the parent quadratic function, f (x) = x^2, is shifted right 6 units and down 2 units. What is the function written in standard form for the translated parabola?

In general the standard form of a parabola is:

(y-k) = a (x-h) ²

Where k indicates the vertical shift & h, the horizontal one.

In your original function f (x) = x², k=h=0. That means the parabola passes by the origine & since a=1>0, it opens up,

Now if you want to shifted it 6 units at the right that means h=6

& 2 units at 2 units down that means k = - 2

Plug these value into the standard form & you will get:

y - (-2) = (x-6) ² or = = > y+2 = (x-6) ² or y = (x-6) ² - 2