Quadratic factors are the algebraic expressions that, when multiplied, result in a quadratic function. A quadratic function has a parabola as its graph and can be written in the standard form: f(x) =
where:
- a determines the opening and direction of the parabola,
- h is the x-coordinate of the vertex,
- k is the y-coordinate of the vertex.
Example
The function f(x) = 
can be factorized as: f(x) = (x−2)(x−3)
Thus, its quadratic factors are (x−2) and (x−3).
Applications:
- Solving quadratic equations (f(x)=0).
- Analysing the roots (solutions) and the intercepts with the x-axis.
- Understanding the shape and properties of parabolas in geometry and calculus.
