It looks like you're working with a quadratic function, and you've provided some details. Here's what I can infer from the information:

• The vertex of the parabola is at $(0, 2)$.
• Since $a > 0$, the parabola opens upwards.

Given this, the general form of a quadratic function is:

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

where $(h, k)$ is the vertex of the parabola. Since the vertex is $(0, 2)$, we can substitute $h = 0$ and $k = 2$:

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

or simplified:

$y = ax^2 + 2$

Since $a > 0$, the parabola will open upwards, and the vertex at $(0, 2)$ will be the minimum point.

Would you like to explore more details, such as finding $a$ if additional points are given?

Here are some related questions:

1. How do you find $a$ if another point on the parabola is provided?
2. What is the axis of symmetry of this parabola?
3. How would the graph change if $a < 0$?
4. How can you determine the direction of a parabola from its equation?
5. How does the vertex form differ from the standard form of a quadratic equation?

Tip: To determine the shape of the parabola, knowing just $a$ (positive or negative) can tell you if it opens upwards or downwards!