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Grade 12 Advanced Functions, University Preparation (MHF4U)
C. Polynomial and Rational Functions
39. 12AF.C3.3
39.5 Shortcut: Vertex formula
Vertex Formula for a Parabola
Skip completing the square: use the vertex formula to jump straight from a quadratic's standard form to its vertex coordinates.
What You'll Learn
The vertex formula finds the vertex of a parabola written in standard form \(y = ax^2 + bx + c\) without completing the square.
The x-coordinate of the vertex is \(x = -\frac{b}{2a}\), and you find the y-coordinate by substituting that value back into the equation.
The vertex formula comes directly from completing the square, so it is really just a faster route to the same answer.
The value \(x = -\frac{b}{2a}\) is also the equation of the parabola's axis of symmetry.
A positive leading coefficient \(a\) gives a minimum vertex, while a negative \(a\) gives a maximum vertex.
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.
This Unit Includes
6 Video lessons
Practice exercises
Learning resources
Skills
Vertex Formula
Quadratic Functions
Vertex Form
General Form
Parabolas
Algebraic Shortcuts
Completing the Square
ON Curriculum Aligned