Unit 3 Vocabulary - Quadratics

Parent Function

Simplest form of a function, like y = x².

Parabola

U-shaped graph of a quadratic.

X-Intercepts

Points where the graph crosses the x-axis.

Y-Intercept

Point where the graph crosses the y-axis.

Vertex

Highest or lowest point of a parabola.

Maximum

Highest point of a parabola (opens down).

Minimum

Lowest point of a parabola (opens up).

Axis of Symmetry

Line that splits a parabola in half.

Factor

Numbers or expressions multiplied to make another.

Terms

Parts of an expression separated by + or -.

Coefficients

Numbers in front of variables.

Zeros

The values of x for which f of x equals zero, synonymous with roots, solutions, and x-intercepts.

Roots

The solutions to f of x equals zero, often found by factoring or using the quadratic formula.

Solutions

The values that satisfy the equation f of x equals zero.

Degree of Polynomials

Highest power of the variable.

Increasing/Decreasing Intervals

Where the graph goes up or down.

End Behavior

Direction the graph goes as x gets very big or small.

Standard Form

Written as ax² + bx + c.

Factored Form

Written as a(x - r₁)(x - r₂).

Vertex Form

Written as a(x-h)² + k.

Greatest Common Factor (GCF)

Biggest number dividing two or more numbers.

Initial Upward Velocity

Speed going up at the start.

Quadratic Formula

Formula to solve ax² + bx + c = 0.

Discriminant

Part of the quadratic formula that shows solution types.

Rational Numbers

Numbers written as fractions.

Irrational Numbers

Numbers that cannot be written as fractions.

Complex Solutions

Solutions with real and imaginary parts.

Imaginary Numbers

Numbers with i, where i² = -1.

Difference of Squares

a² - b², factored as (a+b)(a-b).

Perfect Square Trinomial

Written as (a+b)² or (a-b)².

Extrema

Maximum or minimum points of a graph.

Domain

All possible x-values.

Range

All possible y-values.

Transformations (a, h, k)

Changes in size, position, or shape.

Stretch or Compression

Makes graph narrower (stretch) or wider (compression).

Rate of Change in Quadratics

How fast y-values change as x changes.

Systems of Quadratics

Two or more quadratic equations solved together.

Systems of Quadratic Inequalities

Two or more quadratic inequalities solved together.