Which of the following translations of the graph of `y = x^(2)` would result in the graph of `y = x^(2) - 6x + k` , where k is a constant greater than 10 ?

Options

A. left 6 units and up k units
B. left 3 units and up k + 9 units
C. right 3 units and up k + 9 units
D. right 3 units and up `k -9` units

Explanation

To determine the translation of the graph of \( y = x^2 \) that results in the graph of \( y = x^2 - 6x + k \) (where \( k \) is a constant greater than 10), we will follow these steps:

### Step 1: Rewrite the equation
We start with the equation \( y = x^2 - 6x + k \). Our goal is to complete the square for the quadratic expression \( x^2 - 6x \).