Question

the graph shows g(x), which is a translation of f(x) = x². write the function rule for g(x).
write your answer in the form a(x - h)² + k, where a, h, and k are integers or simplified fractions.
g(x) =

Explanation:

Step1: Identify vertex of $g(x)$

Vertex is $(0, -1)$

Step2: Recall vertex form formula

Vertex form: $g(x)=a(x-h)^2+k$, where $(h,k)$ is vertex

Step3: Substitute vertex values

Substitute $h=0$, $k=-1$: $g(x)=a(x-0)^2-1$

Step4: Determine stretch factor $a$

Since $f(x)=x^2$ has $a=1$, and $g(x)$ has same width, $a=1$. Final form: $g(x)=(x-0)^2-1$

Answer:

$g(x) = (x - 0)^2 - 1$ or $g(x) = x^2 - 1$