Quadratic Equations - Vocabulary Flashcards

Vocabulary flashcards covering key quadratic equation concepts such as form, roots, graph, and solving methods.

Quadratic equation

A polynomial equation of degree 2 in standard form ax^2 + bx + c = 0, with a ≠ 0.

Quadratic (etymology)

From Latin quadraticus meaning squared or of squares.

Standard form (quadratic equation)

ax^2 + bx + c = 0, where a ≠ 0.

Square root

A value that, when squared, equals the original number.

Discriminant

The expression b^2 − 4ac in ax^2 + bx + c = 0; determines the number and type of real solutions.

Quadratic formula

x = [-b ± sqrt(b^2 − 4ac)] / (2a) for ax^2 + bx + c = 0.

Roots

Solutions to the quadratic equation; the x-values where the graph crosses the x-axis.

Real solutions

Solutions that are real numbers; their existence depends on the discriminant.

Completing the square

A method to rewrite a quadratic expression as a(x − h)^2 + k to solve or graph.

General form (quadratic function)

y = ax^2 + bx + c, with a ≠ 0, the expanded form of a quadratic function.

Vertex form

y = a(x − h)^2 + k; the vertex of the parabola is (h, k).

Vertex

The maximum or minimum point of a parabola; coordinates (h, k) in vertex form.

Axis of symmetry

The vertical line x = h that passes through the vertex.

X-intercept

Where the graph crosses the x-axis; solutions to f(x) = 0.

Y-intercept

Where the graph crosses the y-axis; the value f(0).

Parabola

The graph of a quadratic function; a U-shaped curve.

Opens upward

When a > 0, the parabola opens upward (vertex is a minimum).

Opens downward

When a < 0, the parabola opens downward (vertex is a maximum).