Question

what kind of transformation converts the graph of f(x) = -6(x - 4)² into the graph of g(x) = -6(x - 4)² + 4? translation 4 units right translation 4 units left translation 4 units up translation 4 units down

Explanation:

Step1: Recall Vertical Translation Rule

For a function \( y = f(x) + k \), if \( k>0 \), the graph of \( f(x) \) is translated \( k \) units up; if \( k < 0 \), it is translated \( |k| \) units down.
Here, \( f(x)=-6(x - 4)^2 \) and \( g(x)=-6(x - 4)^2+4 \), so we can write \( g(x)=f(x)+4 \).

Step2: Determine the Translation

Since \( k = 4>0 \), according to the vertical translation rule, the graph of \( f(x) \) is translated 4 units up to get the graph of \( g(x) \).

Answer:

translation 4 units up