The problem asks us to identify the vertex and axis of symmetry of a given parabola from its graph, and to determine whether the parabola opens upwards or downwards.
2025/7/3
1. Problem Description
The problem asks us to identify the vertex and axis of symmetry of a given parabola from its graph, and to determine whether the parabola opens upwards or downwards.
2. Solution Steps
Step 1: Identify the vertex. The vertex is the lowest point of the parabola. From the graph, we can see that the vertex is at the point .
Step 2: Identify the axis of symmetry. The axis of symmetry is a vertical line that passes through the vertex of the parabola. The equation of a vertical line is of the form , where is a constant. Since the vertex is at , the axis of symmetry is the vertical line .
Step 3: Determine the direction the parabola opens. From the graph, we can see that the parabola opens upwards.
3. Final Answer
The vertex of the parabola is .
The axis of symmetry is .
The parabola opens upwards.