Quadratic Functions and Equations in One Variable · 1.1.4
Forming quadratic functions
Students translate a real or mathematical situation, such as area, product of numbers, or motion, into a quadratic function f(x) = ax² + bx + c, then connect it to the corresponding quadratic equation f(x) = 0 when a specific output value is required.
The official learning standard (1.1.4)
“Form quadratic functions based on situations, and hence relate them to quadratic equations.”
What it means
Students translate a real or mathematical situation, such as area, product of numbers, or motion, into a quadratic function f(x) = ax² + bx + c, then connect it to the corresponding quadratic equation f(x) = 0 when a specific output value is required.
How it is examined
Commonly tested in Paper 2 as the opening part of a multi-step question, where students first write the quadratic function describing a situation, then solve the related equation. Paper 1 may test simpler direct translations of a described situation into an expression.
Worked example
A rectangular garden has a length that is 3 m more than its width, x m. Form a quadratic function, A(x), for the area of the garden, and write the quadratic equation formed if the area is 40 m².
- Width = x m, Length = (x + 3) m.
- Area, A(x) = x(x + 3) = x² + 3x.
- If the area is 40 m², then A(x) = 40, giving x² + 3x = 40.
- Rearranged into standard form: x² + 3x − 40 = 0.
Source:DSKP KSSM Mathematics Form 4 and 5 (Versi English)
Frequently asked questions
How do I know when to form a function versus an equation?
Form the function first to describe the general relationship in terms of x, such as area A(x). Once a specific value is given, such as the area being 40 m², set the function equal to that value to form the quadratic equation.
What's a common situation used to form quadratic functions?
Common situations include the area of a rectangle whose sides are expressed in terms of x, the product of two consecutive numbers, or distances involving speed and time. Each situation gives an expression that simplifies to ax² + bx + c.
What should I do after forming the function?
Set the function equal to the given output value to form the quadratic equation, then rearrange it into standard form ax² + bx + c = 0 so it is ready to be solved, usually by factorisation.