Question

select the equation that describes the graph shown.\
\
\\(\circ\\ y = x^2 + 5\\)\
\\(\circ\\ y = (x - 5)^2\\)\
\\(\circ\\ y = (x + 5)^2\\)\
\\(\circ\\ y = x^2 - 5\\)

Explanation:

Step1: Recall vertex form of parabola

The vertex form of a parabola is $y=(x-h)^2+k$, where $(h,k)$ is the vertex.

Step2: Identify vertex from graph

The vertex of the parabola is at $(5, 0)$, so $h=5$, $k=0$.

Step3: Substitute into vertex form

Substitute $h=5$ and $k=0$ into the vertex form: $y=(x-5)^2+0=(x-5)^2$.

Step4: Verify with y-intercept

For $x=0$, $y=(0-5)^2=25$, which matches the graph's positive y-intercept.

Answer:

$\boldsymbol{y=(x - 5)^2}$ (Option B)