How to Graph Quadratic Functions (Vertex Form) Definition, Types, Examples & Uses

How to Graph Quadratic Functions (Vertex Form)

Subject: Mathematics

Book: Maths Mastery

A quadratic in vertex form is y = a(x–h)² + k, where (h, k) is the vertex. This format makes identifying vertex location, axis of symmetry (x=h), and direction (a>0 opens up, a<0 opens down) straightforward. For instance, y=2(x–1)²–4 has vertex at (1, –4). Vertex form aids in quick graphing, transformations, and completing the square. You can easily find maxima/minima or intervals of increase/decrease. This approach extends to analyzing parabolas in physics, optimizing business problems, or constructing geometric shapes requiring symmetrical curves.