Question

the graph shown is a translation of the graph of $f(x)=x^{2}$. write the function in vertex form.
$f(x) = \square$
(type your answer in vertex form.)

Explanation:

Step1: Recall vertex form formula

Vertex form of a quadratic function is $f(x) = (x-h)^2 + k$, where $(h,k)$ is the vertex.

Step2: Identify vertex from graph

From the graph, the vertex is at $(3,5)$. So $h=3$, $k=5$.

Step3: Substitute values into vertex form

Substitute $h=3$ and $k=5$ into the vertex form equation.
<Expression>
$f(x) = (x-3)^2 + 5$
</Expression>

Answer:

$f(x) = (x-3)^2 + 5$