Answer:
The horizontal translation of the function is 3 units to the right (from the parent function). Therefore, we subtract 3 from the x-value of the function.
The equation of the graphed function in vertex form is:

Explanation:
The given graph shows a parabola that opens upwards.
Therefore, the equation for this function is a quadratic equation with a positive leading coefficient.
The vertex of a parabola is the minimum point of a parabola that opens upwards, or the maximum point of a parabola that opens downwards.
From inspection of the given graph, the vertex of the function is (3, -2).
The parent function of a parabola that opens upwards is y = x². This has a vertex at (0, 0).
Therefore, given the vertex of the given function is (3, -2), the parent function has been translated 3 units right and 2 units down.
For a horizontal translation to the right, we subtract the number of units from the x-value of the function.
For a vertical translation down, we subtract the number of units from the function.
Therefore, a translation of 3 units right and 2 units down from the parent function y = x² is:

This function is written in vertex form.
To write the equation in standard form, expand the brackets and simplify:




Additional comments
The vertex form of a quadratic equation is y = a(x - h)² + k, where (h, k) is the vertex. Therefore, the "k" value refers to the y-value, which is the vertical translation from the parent function.
As your question refers to the "k" value for the horizontal translation, we assume that it is not referring to the k-value of the vertex form.