Question

Which function represents a parabola that is translated 2 units to the left and 6 units down from the parent function, f(x)=x^2

Answer 1

Translation involves moving a function along its coordinates

The image of the function is $g(x) = (x + 2)^2 - 6$

How to determine the new function

The parent function is given as:

$f(x) = x^2$

When the function is translated 2 units left, we have:

$f'(x) = (x + 2)^2$

When the function is translated 6 units down, we have:

$f"(x) = (x + 2)^2 - 6$

Rewrite as:

$g(x) = (x + 2)^2 - 6$

Hence, the image of the function is $g(x) = (x + 2)^2 - 6$

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