Question

solve the problem.
select the equation that describes the graph shown.
options:

• ( y = (x + 2)^2 - 3 )
• ( y = (x + 3)^2 + 2 )
• ( y = x^2 - 3 )
• ( y = (x - 3)^2 + 2 )

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

From the graph, the vertex is at $(3,2)$, so $h=3$, $k=2$.

Step3: Substitute h and k into vertex form

Substitute $h=3$ and $k=2$ into $y=(x-h)^2+k$:
$y=(x-3)^2+2$

Step4: Verify y-intercept (optional check)

For $x=0$, $y=(0-3)^2+2=9+2=11$, which matches the graph's high y-intercept.

Answer:

$\boldsymbol{y=(x - 3)^2 + 2}$ (the fourth option)