The graph of a quadratic function is a distinctive U-shaped curve called a parabola.
Key Features of a Parabola
Here's a breakdown of its main characteristics:
- Shape: The parabola is characterized by its symmetrical, curved shape. It can open upwards or downwards.
- Vertex: According to the reference, a crucial element is the vertex, which represents the extreme point of the parabola.
- If the parabola opens upwards, the vertex is the lowest point, indicating the minimum value of the quadratic function.
- Conversely, if the parabola opens downwards, the vertex is the highest point, representing the maximum value of the function.
- Axis of Symmetry: This is an imaginary vertical line that passes through the vertex and divides the parabola into two mirror-image halves.
- X-intercept(s): These are the points where the parabola intersects the x-axis. A quadratic function can have zero, one, or two x-intercepts. These are also known as the roots or solutions of the quadratic equation.
- Y-intercept: This is the point where the parabola intersects the y-axis.
Example
Imagine the quadratic function f(x) = x2. Its graph is a parabola that opens upwards. The vertex is at the point (0,0), which represents the minimum value of the function (which is 0).
Summary
| Feature | Description |
|---|---|
| Shape | U-shaped curve |
| Vertex | Extreme point (minimum or maximum) |
| Axis of Symmetry | Vertical line through the vertex, dividing the parabola into two symmetrical halves |
| X-intercept(s) | Points where the parabola crosses the x-axis (roots/solutions) |
| Y-intercept | Point where the parabola crosses the y-axis |
