The problem asks us to find the vertex of the given parabola and then write the equation of the parabola in vertex form.

1. Problem Description

The problem asks us to find the vertex of the given parabola and then write the equation of the parabola in vertex form.

2. Solution Steps

First, we identify the vertex of the parabola from the graph. The vertex is the minimum point of the parabola, which appears to be at $(2, 0)$.

The vertex form of a quadratic equation is given by:

$y = a(x-h)^2 + k$

where $(h, k)$ is the vertex of the parabola.

In this case, the vertex is $(2, 0)$, so $h = 2$ and $k = 0$. Therefore, the equation becomes:

$y = a(x-2)^2 + 0$

$y = a(x-2)^2$

To find the value of $a$, we can use another point on the parabola. Let's use the point $(0, 4)$ which appears to be on the graph.

Substitute $x = 0$ and $y = 4$ into the equation:

$4 = a(0-2)^2$

$4 = a(-2)^2$

$4 = 4a$

$a = 1$

So, the equation of the parabola in vertex form is:

$y = 1(x-2)^2$

$y = (x-2)^2$

3. Final Answer

Vertex of the parabola is $(2, 0)$.

The equation of the parabola in vertex form is $y = (x-2)^2$.