Question

find g(x), where g(x) is the reflection across the y-axis of $f(x) = -5(x + 10)^2 - 1$. write your answer in the form $a(x - h)^2 + k$, where a, h, and k are integers. $g(x) = \square$

Explanation:

Step1: Apply y-axis reflection rule

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

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

Substitute $x=-x$ into $f(x) = -5(x + 10)^2 - 1$:
$g(x) = -5(-x + 10)^2 - 1$

Step3: Rewrite to match target form

Rewrite $(-x + 10)$ as $(x - 10)$ since $-x + 10 = x - (-10)$ is incorrect; correct rearrangement: $-x + 10 = -(x - 10)$, and squaring removes the negative sign:
$g(x) = -5(x - 10)^2 - 1$

Answer:

$g(x) = -5(x - 10)^2 - 1$