The given equation is:

\[
y = x^2 + 2
\]

This is a quadratic function, which describes a parabola. The key features of this parabola are:

1. **Vertex**: The vertex of the parabola is at the point where the function reaches its minimum (or maximum, depending on the direction). Since the coefficient of \( x^2 \) is positive, the parabola opens upwards, and the vertex is the minimum point. In this case, the vertex is at \( (0, 2) \).

2. **Axis of symmetry**: The axis of symmetry is a vertical line that passes through the vertex. For this equation, it is the line \( x = 0 \).

3. **Y-intercept**: The y-intercept occurs where \( x = 0 \). Substituting \( x = 0 \) into the equation gives \( y = 2 \), so the y-intercept is \( (0, 2) \).

4. **Direction of the parabola**: Since the coefficient of \( x^2 \) is positive, the parabola opens upwards.

5. **Shape of the graph**: The parabola will be wider or narrower depending on the value of the coefficient in front of \( x^2 \). In this case, with a coefficient of 1, the graph has a standard shape.

Would you like me to plot this equation or dive into more details?

Here are 5 related questions to consider:

1. What is the general form of a quadratic equation, and how does it differ from this one?
2. How do you find the vertex of a quadratic equation in different forms?
3. What happens to the graph if we change the constant \( +2 \) to another value?
4. How can you solve for \( x \) when \( y \) is a specific value?
5. What is the significance of the axis of symmetry in a parabola?

**Tip**: The vertex form of a quadratic equation, \( y = a(x-h)^2 + k \), is helpful for quickly identifying the vertex and the direction of the parabola.

Explore the properties of the quadratic function y = x^2 + 2, including the vertex at (0, 2), axis of symmetry, and the upward-opening parabola. Ideal for students in Grades 8-10 looking to deepen their understanding of quadratic equations.

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