The equation $y = x^2 + 2$ represents a quadratic function. Let's analyze its properties:

Key Features:

1. Vertex: The vertex of this parabola is at $(0, 2)$. Since the coefficient of $x^2$ is positive, the parabola opens upwards.
2. Axis of Symmetry: The axis of symmetry is the vertical line $x = 0$ (or the y-axis).
3. Y-intercept: The y-intercept is the point where the graph intersects the y-axis. In this case, it is at $(0, 2)$.
4. X-intercepts: To find the x-intercepts, set $y = 0$ and solve for $x$: $x^2 + 2 = 0 \implies x^2 = -2$ Since $x^2 = -2$ has no real solutions, this parabola does not intersect the x-axis.
5. Direction: The parabola opens upwards because the coefficient of the $x^2$ term is positive.

Would you like more details or have any questions about this?

Here are 5 questions related to this quadratic function:

1. What is the significance of the vertex in a parabola?
2. How do you determine if a quadratic function opens upwards or downwards?
3. What methods can be used to find the x-intercepts of a quadratic function?
4. How does the constant term in a quadratic equation affect its graph?
5. Can a quadratic function have complex x-intercepts, and how are they interpreted?

Tip: When graphing a quadratic equation, always start by locating its vertex and axis of symmetry to understand its shape and orientation.