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
Answer
Explanation:
Step1: Recall translation rule
For a quadratic function in vertex - form $y = a(x - h)^2+k$, the horizontal translation of the parent function $y=x^2$ is determined by the value of $h$. The parent function $y = x^2$ is translated $h$ units to the right if $h>0$ and $|h|$ units to the left if $h < 0$.
Step2: Identify $h$ value
The function $g(x)=(x - 4)^2+2$ is in the form $y=a(x - h)^2 + k$, where $a = 1$, $h = 4$, and $k=2$. The horizontal translation is based on the value of $h$.
Answer:
4