what value represents the horizontal translation from the graph of the parent function ( f(x)=x^{2} ) to the…

what value represents the horizontal translation from the graph of the parent function ( f(x)=x^{2} ) to the graph of the function ( g(x)=(x - 4)^{2}+2 )?\n-4\n-2\n2\n4

what value represents the horizontal translation from the graph of the parent function ( f(x)=x^{2} ) to the graph of the function ( g(x)=(x - 4)^{2}+2 )?\n-4\n-2\n2\n4

Answer

Explanation:

Step1: Recall the transformation rule for horizontal translation

For a function (y = f(x - h)+k), the horizontal translation is determined by (h). If (h>0), the graph of (y = f(x)) is shifted to the right by (h) units. If (h < 0), the graph of (y=f(x)) is shifted to the left by (|h|) units. The parent function is (f(x)=x^{2}) and the transformed function is (g(x)=(x - 4)^{2}+2). Comparing (g(x)) with the form (y=(x - h)^{2}+k) (where the parent function is (y = x^{2})), we have (h = 4) and (k=2).

Answer:

(4)