Answer:
f(x) = x^2 -3
Step-by-step explanation:
A function is translated down 3 units by subtracting 3 from the function value. For the parent function f(x) = x^2, the translated function is ...
f(x) = x^2 -3
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<em>Comment on vertex form</em>
The full "vertex form" has the values of the vertex coordinates in the equation explicitly. For vertex (h, k), the form is ...
f(x) = a(x -h)^2 +k
We have moved the vertex from (0, 0) to (0, -3). The vertical scale factor (a) remains 1. So, we could write the equation as ...
f(x) = 1(x -0)^2 -3 . . . . vertex form with unnecessary parts shown
Removing the identity elements doesn't change anything (though it requires a little practice to see them when they aren't there). So, with minor simplification, this becomes ...
f(x) = x^2 -3
