Back

Quadratic Functions: Vertex, Zeros, and Forms

SAT MathAdvanced MathMedium

Extract the useful feature from standard, vertex, or factored form.

What you need to know

  • Standard form ax² + bx + c shows y-intercept c and opening direction.
  • Vertex form a(x − h)² + k shows vertex (h, k).
  • Factored form a(x − r₁)(x − r₂) shows zeros.
  • The axis of symmetry is x = −b/(2a), halfway between real zeros.

The AYLOTI method

  1. Identify the form given.
  2. Read the visible feature directly.
  3. Convert only if another feature is needed.
  4. Interpret the feature in context.

AYLOTI • Sir Hunain Zia • SAT Score 1594/1600 • 154 Total A Grades (Personal), 11 World Records, 7 Distinctions

Worked example

For f(x) = −2(x − 3)² + 8, state the vertex and maximum.

  1. Vertex form gives h = 3 and k = 8.
  2. a = −2, so the parabola opens downward.
  3. The vertex is therefore the maximum point.

Answer: Vertex (3, 8); maximum value 8.

Common SAT traps

  • Reading vertex x-coordinate as −h.
  • Assuming every vertex is a minimum.
  • Confusing zeros with the y-intercept.
Quick check

What are the zeros of (x + 5)(x − 2)?

x = −5 and x = 2.

Before you move on

  • Explain the core rule without looking back.
  • Redo the worked example using your own steps.
  • Write the trap you are most likely to fall for.
author avatar