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SPM Mathematics Glossary

Quadratic Functions and Equations in One Variable, terms

Quadratic functionA function of the form y = ax² + bx + c, where a is not zero; its graph is a parabola.Root of an equationA value of x that makes the equation equal to zero; where the graph meets the x-axis.DiscriminantThe value b² − 4ac, whose sign tells you how many real roots a quadratic equation has.ParabolaThe U-shaped curve of a quadratic function; it opens upward if a is positive and downward if a is negative.CoefficientThe number multiplying a variable; in ax² + bx + c the coefficients are a, b and c.Turning pointThe maximum or minimum point of a parabola, found by completing the square.Axis of symmetryThe vertical line through the turning point that divides a parabola into two mirror halves.Nature of rootsWhether a quadratic has two, one or no real roots, decided by the discriminant b² − 4ac.VariableA symbol, usually a letter, standing for a number that can change.

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Frequently asked questions

What's the difference between a "root" and the "turning point" of a quadratic?

A root is a value of x where the quadratic equals zero, where the parabola crosses the x-axis, and there can be up to two of them. The turning point is the single highest or lowest point on the parabola's curve, found using the axis of symmetry; a quadratic can have two roots but only ever one turning point.

Out of all the quadratic terms, which should I learn first?

Start with "quadratic function" and "coefficient" so you can read the standard form ax² + bx + c correctly, then move to "root" and "parabola" since most questions ask you to find roots or describe the graph's shape. "Discriminant", "nature of roots", "turning point" and "axis of symmetry" build on those basics and are easier once the first group is solid.

How does the "discriminant" tell me about the "nature of roots"?

The discriminant is the value b² − 4ac from the quadratic formula, and its sign tells you what kind of roots the equation has without solving it fully: positive means two different real roots, zero means one repeated root (the parabola just touches the x-axis), and negative means no real roots at all. Examiners often ask you to state the nature of roots using only this value.

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