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

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