To find the vertex and axis of symmetry of a quadratic function in the standard form \(y = ax^2 + bx + c\), follow these steps:
1. **Vertex:**
- The x-coordinate of the vertex of a quadratic function in the standard form \(y = ax^2 + bx + c\) can be found using the formula \(-\frac{b}{2a}\).
- Substitute this x-coordinate back into the function to find the y-coordinate of the vertex.
- The vertex of the quadratic function is the point \((h, k)\), where \(h\) is the x-coordinate and \(k\) is the y-coordinate.
2. **Axis of Symmetry:**
- The axis of symmetry of a quadratic function is a vertical line that passes through the vertex.
- The equation of the axis of symmetry is \(x = h\), where \(h\) is the x-coordinate of the vertex.
- This line divides the parabola into two symmetric parts.
By following these steps, you can determine the vertex and axis of symmetry of a quadratic function given in the standard form. Remember that the vertex represents the maximum or minimum point of the parabola, while the axis of symmetry is the line that divides the parabola into two equal halves.
