SAT-35: Vertex Form of a Quadratic

SAT-35: Vertex Form of a Quadratic

Description: A parabola has a turning point called the vertex. Vertex form lets you read that point directly, with no calculation. The SAT loves this.

The Form

y = a(x − h)² + k, where the vertex is the point (h, k).

(Oʻzbekcha: uch koʻrinishida parabolaning uchi (choʻqqisi) (h, k) nuqtasi boʻladi.)

Watch the sign of h carefully. The form has (x − h), so:

• y = (x − 3)² + 2 → h = 3, k = 2 → vertex (3, 2).
• y = (x + 4)² − 1 → this is (x − (−4))² − 1 → vertex (−4, −1).

(Oʻzbekcha: x + 4 aslida x − (−4), shuning uchun h = −4.)

What "a" tells you

• a > 0 → parabola opens up → vertex is the lowest point (minimum).
• a < 0 → parabola opens down → vertex is the highest point (maximum).

(Oʻzbekcha: a > 0 boʻlsa parabola yuqoriga ochiladi (eng kichik nuqta), a < 0 boʻlsa pastga ochiladi (eng katta nuqta).)

Vertex form vs standard form

• Standard: y = ax² + bx + c — easy to see the y-intercept (c).
• Vertex: y = a(x − h)² + k — easy to see the vertex (h, k).

Practice

What is the vertex of y = −2(x − 5)² + 7, and is it a max or min?

Key words — Kalit soʻzlar

• Vertex — uch (choʻqqi)
• Vertex form — uch koʻrinishi
• Parabola — parabola
• Turning point — burilish nuqtasi
• Minimum — eng kichik qiymat
• Maximum — eng katta qiymat
• Opens up — yuqoriga ochiladi
• Opens down — pastga ochiladi
• Standard form — standart koʻrinish
• y-intercept — y oʻqini kesish nuqtasi

Summary

• Vertex form: y = a(x − h)² + k, vertex = (h, k).
• Sign trick: (x + 4) means h = −4.
• a > 0 opens up (minimum); a < 0 opens down (maximum).