Math 2 Unit 3: Quadratics Quizlet

Parent Function

The simplest form of a function in a family. For quadratics, it is f of x equals x squared.

Parabola

The graph of a quadratic function, which is a symmetric U-shaped curve.

x-Intercepts

Points where the graph crosses the x-axis, found by solving f of x equals zero. Synonymous with roots, zeroes, and solutions.

y-intercept

The point where the graph crosses the y-axis, found by evaluating f of zero.

Vertex

The highest or lowest point of a parabola, located at negative b over two a and its corresponding y-value.

Maximum

The highest value of a function, occurring at the vertex for a downward-opening parabola when a is less than zero.

Minimum

The lowest value of a function, occurring at the vertex for an upward-opening parabola when a is greater than zero.

Axis of Symmetry

A vertical line passing through the vertex of a parabola, given by x equals negative b over two a.

Factor

An expression that divides another expression without a remainder, such as x minus p and x minus q being factors of a quadratic equation.

Terms

The individual components of a polynomial, separated by addition or subtraction. For example, in three x squared plus two x plus one, the terms are three x squared, two x, and one.

Coefficients

The numerical factors of terms in a polynomial, such as three in three x squared.

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

The highest power of the variable in a polynomial. For example, two for five x squared plus three x plus one.

Increasing or Decreasing Intervals

Intervals where the function's value is rising, known as increasing, or falling, known as decreasing.

End Behavior

The behavior of f of x as x approaches positive infinity or negative infinity.

Standard Form

A quadratic equation written as y equals a x squared plus b x plus c.

Factored Form

A quadratic equation written as y equals a times x minus p times x minus q.

Vertex Form

A quadratic equation written as y equals a times x minus h squared plus k, where h and k are the coordinates of the vertex.

Greatest Common Factor (GCF)

The largest factor common to all terms of a polynomial.

Initial Upward Velocity

The initial velocity, represented as v subscript zero, in vertical motion problems modeled by h of t equals negative one-half times g times t squared plus v subscript zero times t plus h subscript zero.

Quadratic Formula

The formula x equals negative b plus or minus the square root of b squared minus four a c all over two a, used to find the roots of a quadratic equation.

Discriminant

The expression b squared minus four a c in the quadratic formula, which determines the nature of the roots.

Rational Numbers

Numbers that can be expressed as a fraction of two integers, where the denominator is not zero.

Irrational Numbers

Numbers that cannot be expressed as a fraction of two integers, such as the square root of two.

Complex Solutions

Solutions to equations that include imaginary numbers, such as three plus two i.

Imaginary Numbers

Numbers involving i, where i is defined as the square root of negative one.

Difference of Squares

A binomial of the form a squared minus b squared, which can be factored as a minus b times a plus b.

Perfect Square Trinomial

A trinomial that is the square of a binomial, such as a plus b squared equals a squared plus two a b plus b squared.

Extrema

The maximum and minimum values of a function.

Domain

The set of all possible input values, typically the x-values, for a function.

Range

The set of all possible output values, typically the y-values, for a function.

Transformations, a, h, and k

Parameters in the vertex form of a quadratic equation that stretch, shift, or compress the graph.

a, Stretch, Compression

When a is greater than one, the graph stretches. When a is between zero and one, the graph compresses.

Rate of Change in Quadratics

The change in y-values relative to x, which varies for quadratics and is not constant.

Systems of Quadratics

Sets of equations involving quadratic functions solved together, such as y equals a x squared plus b x plus c and y equals d x squared plus e x plus f.

Systems of Quadratic Inequalities

Inequalities involving quadratics, such as y is greater than or equal to a x squared plus b x plus c, solved by finding overlapping solution regions.