Chapter 11.4

Shortcut: Vertex formula

What You'll Learn

Apply the vertex formula x = -b/(2a) to find the x-coordinate of a parabola's vertex
Calculate the y-coordinate by substituting the x-value back into the quadratic equation
Convert quadratic functions from general form to vertex form using the vertex formula
Relate the vertex formula to the quadratic formula to aid memorization
Derive the vertex formula by completing the square on a general quadratic expression

What You'll Practice

1

Finding vertices using the shortcut formula instead of completing the square

2

Converting equations like y = 2x² - 12x + 10 from general to vertex form

3

Working with fractional coefficients and negative leading coefficients

4

Simplifying expressions with least common denominators to find y-coordinates

Why This Matters

The vertex formula is a powerful shortcut that saves you significant time on tests and homework. Instead of completing the square every time, you can find the vertex of any parabola in secondsessential for graphing, optimization problems, and higher-level math courses.

Before You Start — Make Sure You Can:

Quadratic function in general form: y = ax^2 + bx + cQuadratic function in vertex form: y = a(x-p)^2 + qCompleting the squareConverting from general to vertex form by completing the square

This Unit Includes

6 Video lessons
Practice exercises

Skills

Vertex Formula
Quadratic Functions
Vertex Form
General Form
Parabolas
Algebraic Shortcuts
Completing the Square
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