Question

find $g(x)$, where $g(x)$ is the reflection across the $y$-axis of $f(x) = 5(x - 1)^2 + 8$. write your answer in the form $a(x - h)^2 + k$, where $a$, $h$, and $k$ are integers. $g(x) = \square$

Explanation:

Step1: Recall y-axis reflection rule

To reflect a function $f(x)$ across the y-axis, replace $x$ with $-x$ in the function, so $g(x)=f(-x)$.

Step2: Substitute $-x$ into $f(x)$

$$g(x)=5(-x - 1)^2 + 8$$

Step3: Rewrite the binomial

Factor out $-1$ from the parentheses to match the form $a(x-h)^2 + k$:
$$-x - 1 = -(x + 1) = (x - (-1))$$
Substitute back:
$$g(x)=5(x - (-1))^2 + 8$$

Answer:

$5(x + 1)^2 + 8$