Quadratic Equations and Parabola Concepts

Vocabulary flashcards covering core terms related to quadratic equations and their parabolic graphs.

Discriminant

The expression b² − 4ac in a quadratic equation; determines the nature and number of roots.

Product of Roots

For ax² + bx + c = 0, the product αβ equals c/a.

Parabola

The U-shaped curve that represents the graph of a quadratic function.

Axis of Symmetry

The vertical line that divides a parabola into two mirror-image halves.

y-Intercept

The y-coordinate where the graph crosses the y-axis.

Roots of a Parabola

The x-values where the graph intersects the x-axis (also called zeros or solutions).

Vertex

The highest or lowest point on a parabola; the point where the axis of symmetry meets the curve.

Maximum

The highest point of a downward-opening parabola.

Minimum

The lowest point of an upward-opening parabola.

Concavity

Indicates whether the parabola opens upward (concave up) or downward (concave down).

Roots of a Quadratic Equation

The two solutions, typically denoted α and β, that satisfy ax² + bx + c = 0.

Sum of Roots

For ax² + bx + c = 0, the sum α + β equals −b/a.

Axis of Symmetry Formula

Given y = ax² + bx + c, the axis of symmetry is x = −b / (2a).

Axis of Symmetry from Roots

Can be found as the average of the roots: x = (α + β) / 2.