3) $$ y=1 / 2 x^{2} $$ Axis of symmetry: Vertex: Roots: Max or Min:

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To analyze the quadratic function $$ y = \frac{1}{2} x^2 $$, we can identify the following characteristics:

1. **Axis of Symmetry**: The axis of symmetry for a quadratic function in the form $$ y = ax^2 + bx + c $$ is given by the formula $$ x = -\frac{b}{2a} $$. In this case, $$ a = \frac{1}{2} $$ and $$ b = 0 $$. Therefore, the axis of symmetry is:
   $$
   x = -\frac{0}{2 \cdot \frac{1}{2}} = 0
   $$

2. **Vertex**: The vertex of the parabola can be found using the axis of symmetry. Since the axis of symmetry is $$ x = 0 $$, we can find the y-coordinate of the vertex by substituting $$ x = 0 $$ into the function:
   $$
   y = \frac{1}{2}(0)^2 = 0
   $$
   Thus, the vertex is at the point $$ (0, 0) $$.

3. **Roots**: To find the roots of the function, we set $$ y = 0 $$:
   $$
   0 = \frac{1}{2} x^2
   $$
   This simplifies to:
   $$
   x^2 = 0 \implies x = 0
   $$
   Therefore, there is one root at $$ x = 0 $$.

4. **Max or Min**: Since the coefficient $$ a = \frac{1}{2} $$ is positive, the parabola opens upwards. This means that the vertex represents a minimum point. Therefore, the function has a minimum value at the vertex, which is $$ y = 0 $$.

In summary:
- **Axis of symmetry**: $$ x = 0 $$
- **Vertex**: $$ (0, 0) $$
- **Roots**: $$ x = 0 $$
- **Max or Min**: Minimum (at $$ y = 0 $$)
Axis of symmetry: $$ x = 0 $$ Vertex: $$ (0, 0) $$ Roots: $$ x = 0 $$ Max or Min: Minimum (at $$ y = 0 $$)

Axis of symmetry:
Vertex:
Roots:
Max or Min:

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