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SingaporeAdditional Mathematics

Quadratic Functions and Equations

4 dot points across 4 inquiry questions. Click any dot point for a focused answer with worked past exam questions where available.

What does the discriminant tell us about the number and type of roots of a quadratic equation?

Use the discriminant b squared minus 4ac to determine whether a quadratic has two, one or no real roots and to solve related problems
A focused answer to the O-Level A-Maths outcome on the discriminant. Using b squared minus 4ac to decide the number of real roots and to find unknown constants for given root conditions.
8 min answer →

How can a substitution turn a non-quadratic equation into a quadratic we already know how to solve?

Solve equations reducible to quadratic form by a suitable substitution, including equations in powers, surds and exponentials
A focused answer to the O-Level A-Maths outcome on equations reducible to quadratic form. Choosing a substitution, solving the resulting quadratic, and reverting to find every valid solution.
8 min answer →

How does completing the square reveal the maximum or minimum value and the line of symmetry of a quadratic?

Express a quadratic in completed-square form and use it to find the vertex, the maximum or minimum value, and the line of symmetry
A focused answer to the O-Level A-Maths outcome on quadratic functions. Completing the square to find the vertex, the maximum or minimum value, and the line of symmetry, and sketching the parabola.
9 min answer →

How do we solve a quadratic inequality and express the solution as a range of values?

Solve quadratic inequalities by factorising and reasoning about the sign of the quadratic between and beyond its roots
A focused answer to the O-Level A-Maths outcome on quadratic inequalities. Factorising, locating the roots, and using a sketch or sign reasoning to read off the solution range.
8 min answer →