Algebra 2 Vocabulary Flashcards

Study Notes

Standard Form of a Quadratic Function

A quadratic function is expressed as f(x) = ax² + bx + c, where a, b, c are real numbers and a ≠ 0.
The graph of a quadratic function is called a parabola.

Parabola

A parabola is a symmetrical open plane curve formed by the intersection of a cone and a plane parallel to its side.
The trajectory of a projectile under gravity ideally follows a parabolic path.

Vertex Form

The vertex form of a quadratic function is f(x) = a(x - h)² + k, with (h, k) representing the vertex of the parabola.
Different textbooks may interpret "standard form" of a quadratic function variably.

Intercept Form

Slope-intercept form is y = mx + b, where m represents the slope and b is the y-intercept.

Quadratic Equation

A quadratic equation is defined as an equation of degree 2, with the highest exponent being 2.
The standard form is expressed as y = ax² + bx + c, where a cannot be zero.

Root of an Equation

A real number x is considered a root if it satisfies the equation.
Roots correspond to the x-intercepts of the quadratic function, indicating intersection points with the x-axis.

Zero of an Equation

A zero of a function is an input value that results in an output of zero.
Zeros are identified as the x-coordinates where the graph intersects the x-axis, also known as x-intercepts.

Square Root

A square root of a number a is a number y such that y² = a.
For instance, both 4 and -4 are square roots of 16 since (4)² = (−4)² = 16.

Complex Numbers

A complex number is expressed in the form a + bi, where a and b are real numbers, and i is the imaginary unit satisfying i² = -1.
In a complex number, a represents the real part, while b denotes the imaginary part.

Imaginary Numbers

Imaginary numbers can be represented as a real number multiplied by the imaginary unit i, defined by i² = -1.
For example, 5i is an imaginary number, and its square results in -25.

Completing the Square

Completing the square is a method for solving quadratic equations, graphing quadratic functions, and evaluating integrals.
It is particularly useful when factoring does not yield sufficient results or to find irrational and complex roots.

Quadratic Formula

The quadratic formula is utilized to solve quadratic equations and is represented as x = (-b ± √D) / (2a).
A quadratic equation typically has two solutions, which are referred to as roots.

Discriminant

The discriminant D = b² - 4ac is calculated from the coefficients of the equation ax² + bx + c = 0.
The discriminant indicates the nature and type of roots the quadratic equation possesses.

Description

Test your knowledge of key terms in Algebra 2 with these flashcards. This quiz covers important concepts such as the standard form of a quadratic function and the definition of a parabola. Perfect for students looking to reinforce their understanding of algebra vocabulary.