The equation you've provided is:

$y = x^2 + 3$

This represents a quadratic function. Let's break it down:

1. Parabola: The graph of this equation is a parabola, opening upwards, since the coefficient of $x^2$ is positive.
2. Vertex: The vertex of the parabola is at $(0, 3)$, because the constant term $+3$ shifts the graph upwards by 3 units.
3. Axis of symmetry: The axis of symmetry is the vertical line $x = 0$, which passes through the vertex.
4. Y-intercept: The y-intercept is at $(0, 3)$, because when $x = 0$, $y = 3$.
5. X-intercepts: There are no real x-intercepts, as the equation $x^2 + 3 = 0$ does not have real solutions (it only has complex solutions).

Would you like more details or have any questions?

Here are five questions related to this:

1. How would the graph change if we modified the equation to $y = x^2 - 3$?
2. What are the complex solutions to the equation $x^2 + 3 = 0$?
3. How does the value of the constant term affect the graph of a quadratic equation?
4. Can you describe how to find the axis of symmetry for any quadratic function?
5. What is the general form of a quadratic equation?

Tip: For quadratic equations, the vertex form is useful for identifying the vertex and transformations of the graph easily!