Study guides › Level 8 · Algebra 2

The vertex of a parabola

Level 8 · Algebra 2 · for questions like “Where is the lowest point of y = (x − 3)² + 2?”

💡 The idea

• y = (x − h)² + k has its vertex (turning point) at (h, k).
• For y = x² + bx + c, the vertex's x is −b ÷ 2. Put it back in to get y.

✏️ Worked examples

1. y = (x − 3)² + 2: the vertex is (3, 2).

2. y = (x + 4)² − 1: the vertex is (−4, −1).

3. y = x² − 6x + 11: x = 6 ÷ 2 = 3, and y = 9 − 18 + 11 = 2. The vertex is (3, 2).

⚠️ Watch out

• The sign inside the bracket flips: (x + 4) means h = −4.

🎯 Try these

1. y = (x − 5)² + 7
2. y = (x + 2)² − 3
3. y = x² + 8x + 20

Answers: 1) (5, 7) 2) (−2, −3) 3) (−4, 4)

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