Overview
Watch
Read
Next Steps
Overview
Advanced Mathematics 2200
Relations and Functions
6. NL.SO.2200RF3
6.8 Quadratic function in vertex form: y = a(x-p)^2 + q
Quadratic Function in Vertex Form
See how y equals a times x minus p squared plus q reveals a parabola's vertex, axis of symmetry, and direction of opening, with graphed examples.
What You'll Learn
Vertex form writes a quadratic function as y equals a times the quantity x minus p squared plus q
The vertex of the parabola is the point p, q, and the axis of symmetry is the vertical line x equals p
The sign of a tells you whether the parabola opens upward or downward and how narrow or wide it is
Vertex form can be expanded into general form, or general form can be converted to vertex form by completing the square
Reading a, p, and q directly from the equation makes graphing a quadratic function faster than using general form
What You'll Practice
1
Finding vertices by making both brackets equal zero
2
Solving for x-intercepts using square root methods with plus-minus signs
3
Calculating y-intercepts by substituting x = 0
4
Graphing parabolas using vertex and intercepts
Why This Matters
Vertex form is one of the most powerful ways to analyze quadratic functions because it reveals the vertex instantly. You'll use this form throughout algebra, precalculus, and calculus to optimize real-world problems like projectile motion, profit maximization, and engineering design.
This Unit Includes
1 Video lesson
Learning resources
Skills
Vertex Form
Quadratic Functions
Parabolas
Intercepts
Square Roots
Graphing
Algebra
NL Curriculum Aligned