Algebra II - Module 3 Vocabulary

Study Notes

Algebra II - Module 3 Vocabulary

Axis of Symmetry: Designates the vertical line that divides the graph into two mirror-image halves, significant in understanding the parabolic shape of quadratic functions.
Completing the Square: Involves rearranging a quadratic expression to form a perfect square trinomial, facilitating the solution of quadratic equations and analysis of graph properties.
Complex Conjugate: Two complex numbers represented as (a + bi) and (a - bi), essential for simplifying expressions and solving polynomial equations involving imaginary numbers.
Complex Number: Any number expressible in the form (a + bi), where (a) and (b) are real numbers, and (i) is the imaginary unit, expanding the number system to include solutions to all polynomial equations.
Factored Form: A quadratic equation written as (0 = a(x-p)(x-q)), clearly indicating the x-intercepts (p) and (q) of the graph, which aids in graphing and analyzing quadratic functions.
Imaginary Unit: Defined as the principal square root of -1, denoted as (i), serving as the foundation for complex numbers and facilitating operations involving negative square roots.
Pure Imaginary Number: Contains the form (bi) where (b) is a real number. These numbers exist solely along the imaginary axis in the complex plane.
Quadratic Inequality: An expression involving a quadratic that is set as an inequality. This concept is crucial for determining ranges of x-values that satisfy certain conditions within a quadratic function.
Quadratic Relations: Describes equations representing parabolas with horizontal axes of symmetry, distinguishing them from functions since they do not pass the vertical line test.
Rationalizing a Denominator: A technique that eliminates radicals from the denominator of a fraction, enhancing the simplicity and clarity of mathematical expressions.
Standard Form: A quadratic equation presented as (ax^2 + bx + c = 0), where (a) cannot equal zero. This standardization is crucial for identifying coefficients and understanding the parabola’s properties.
Vertex: Refers to the peak or lowest point of a parabola, which plays a vital role in determining the maximum or minimum values of the quadratic function.
Vertex Form: Expresses a quadratic function as (f(x) = a(x-h)^2 + k), where ( (h, k) ) denotes the vertex, making it useful for graphing and understanding the function's transformations.