Quadratic Function
See It in Action
Two examples of the idea done right—and one common look-alike that is not right.
EXAMPLE
EXAMPLE
NON-EXAMPLE
Definition
A quadratic function is a function that can be written in the form:
y = ax^2 + bx + c
where:
a, b, and c are constants, and a does not equal 0 (because if a = 0, it would no longer be a quadratic function, but a linear function).
x is the independent variable.
Key characteristics of a quadratic function:
Degree: The highest power of x is 2, which makes the function a degree 2 polynomial.
Graph: The graph of a quadratic function is a parabola. It can either open upward (if a > 0) or downward (if a < 0).
Vertex: The function has a vertex, which is the point where the parabola reaches its highest or lowest value.
Axis of symmetry: The graph is symmetric around a vertical line called the axis of symmetry, which passes through the vertex.
Example:
The quadratic function y = 2x^2 -4x + 1 is a quadratic function. It has:
A degree of 2 (the highest power of x is 2),
A parabolic shape that opens upward because a = 2 is positive,
A vertex and axis of symmetry that can be calculated.