A function that has an equation of the form y = ax² + bx + c where a does not equal 0.
A quadratic function is a type of function where the highest exponent on the variable is 2. It is usually written as y = ax² + bx + c, where:
- a, b, and c are numbers
- a ≠ 0
- x² means “x squared”
The graph of a quadratic function is called a parabola, and it has a U-shape. The parabola can open upward or downward depending on whether a is positive or negative.
For example:
- y = x²
- y = 2x² + 3x − 1
- y = −x² + 4
Quadratic functions are useful because they help us model:
- The path of a ball thrown into the air
- Maximum and minimum values
- Area and optimization problems
When Do Students Learn About Quadratic Functions?
Students begin learning about quadratic functions after developing skills in algebra.
Grades 8–9 – Introduction to Quadratics
Students learn to recognize quadratic expressions and graph simple parabolas.
Grades 10+ – Working with Quadratic Functions
Students solve quadratic equations using factoring, completing the square, and the quadratic formula. They analyze graphs and real-world applications.
