If kgt4 is a constant, how would you translate the graph of `y=x^(2)` to get the graph of `y=x^(2)+4x+k`?

Options

A. left 2 units and up k units
B. right 2 units and up (k-4) units
C. left 2 units and up (k-4) units
D. right 2 units and down (k-4) units

Explanation

To translate the graph of \( y = x^2 \) to obtain the graph of \( y = x^2 + 4x + k \), we can follow these steps:

### Step 1: Rewrite the function
Start with the function \( y = x^2 + 4x + k \). We want to complete the square for the quadratic part \( x^2 + 4x \).

### Step 2: Complete the square
To complete the square for \( x^2 + 4x \), we can rewrite it as follows:
\[ y = (x^2 + 4x + 4) + k - 4 \]
This simplifies to:
\[ y = (x + 2)^2 + (k - 4) \]

### Step 3: Identify the transformations
Now, we can see that the function \( y = (x + 2)^2 + (k - 4) \) indicates two transformations:
1. The term \( (x + 2)^2 \) shows that the graph of \( y = x^2 \) has been translated **left by 2 units**.
2. The term \( (k - 4) \) indicates that the graph has been translated **up by \( k - 4 \) units**.

### Conclusion
Thus, to translate the graph of \( y = x^2 \) to get \( y = x^2 + 4x + k \), we translate it left by 2 units and up by \( k - 4 \) units.

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