The Quadratic Function and its Graphic (The Parabola)
Lesson Summary
When substituting the x variable from -3 to 3 in the function y = x², we get the following values:
Values of x and y
| x | y |
|---|---|
| 0 | 0 |
| 1 | 1 |
| 2 | 4 |
| 3 | 9 |
| -1 | 1 |
| -2 | 4 |
| -3 | 9 |
These values can be plotted on a coordinate system, and when connected by a smooth curve, they form a parabola.
A parabola is the graphical representation of a quadratic function and has the following properties:
- It has a minimum or maximum point corresponding to its vertex, depending on whether it opens up or down.
- The vertex is the most important point on the parabola.
- The parabola is symmetric, mirroring itself along the axis of symmetry.
- An imaginary line passing through the vertex serves as the axis of symmetry.
- The vertex is represented by the coordinates h (x-coordinate) and k (y-coordinate).
The equation of the axis of symmetry is x = h, where h is the vertex's x-coordinate.
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