Graphing Parabolas
Graph y = x²
| x | y = x² |
|---|---|
| -2 | 4 |
| -1 | 1 |
| 0 | 0 |
| 1 | 1 |
| 2 | 4 |
1. Vertical Translation
y = x² + k
If k > 0, y = x² moves upward k units.
If k < 0, y = x² moves down k units.
The vertex of the parabola is: (0, k).
The axis of symmetry is: x = 0.
y = x² + 2 y = x² − 2
2. Horizontal Translation
y = (x + h)²
If h > 0, y = x² is shifted to the left h units.
If h < 0, y = x² is shifted to the right h units.
The vertex of the parabola is: (−h, 0).
The axis of symmetry is: x = −h.
y = (x + 2)²y = (x − 2)²
3. Oblique Translation
y = (x + h)² + k
The vertex of the parabola is: (−h, k).
The axis of symmetry is: x = −h.
y = (x − 2)² + 2 y = (x + 2)² − 2
