Graphing Parabolas

Graph y = x²

x y = x²
-2 4
-1 1
0 0
1 1
2 4

Parabola

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.

Vertical TranslationVertical Translation

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.

Horizontal TranslationHorizontal Translation

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.

Oblique TranslationOblique Translation

y = (x − 2)² + 2 y = (x + 2)² − 2