A Level Math P1: Quadratics Summary

Vocabulary flashcards covering core quadratic concepts for A Level Math P1, including formulas, root properties, graphing features, and practical applications.

Quadratic equation

A second-degree polynomial typically written in the form $ax^2 + bx + c = 0$, where $a \neq 0$ and $b$ and $c$ are constants.

Quadratic formula

The formula $x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$, used to determine the solutions of a quadratic equation.

Discriminant ($D$)

The expression $D = b^2 - 4ac$, which determines the nature of the roots of a quadratic equation.

Discriminant condition: $D > 0$

Indicates that the quadratic equation has two distinct real roots.

Discriminant condition: $D = 0$

Indicates that the quadratic equation has one repeated real root.

Discriminant condition: $D < 0$

Indicates that the quadratic equation has no real roots (two complex roots).

Factoring quadratics

The method of rewriting a quadratic expression as the product of two binomials, such as writing $x^2 + 5x + 6$ as $(x + 2)(x + 3)$.

Parabola

The characteristic shape of a quadratic function's graph, which opens upwards if $a > 0$ and downwards if $a < 0$.

Vertex

The minimum or maximum point of a quadratic function's graph.

Axis of symmetry

The vertical line given by $x = -\frac{b}{2a}$, where the vertex's y-coordinate can be found by substituting this x-value into the quadratic equation.

Projectile motion (quadratic application)

A real-world application of quadratic equations used for modeling the trajectory of objects under gravity.

Optimization problems (quadratic application)

An application of quadratics focused on finding maximum or minimum values in real-life scenarios.

Geometry problems (quadratic application)

Problems involving areas of shapes that are defined by quadratic equations.