Algebra 2 Chapter 5 Flashcards

Quadratic Functions and Properties

• A quadratic function is represented as f(x) = a(x - h)² + k, where a ≠ 0.
• The parabola is the graph of a quadratic function, characterized by its U-shape.

Key Features of Parabolas

• The axis of symmetry is a vertical line that runs through the vertex, dividing the parabola into two equal parts.
• The vertex is the highest or lowest point of the parabola, indicating the maximum or minimum value depending on its orientation.

Standard Forms and Types

• Standard form of a quadratic function is given by f(x) = ax² + bx + c.
• Binomials are quadratic expressions featuring two terms.
• Trinomials consist of three terms, representing more complex quadratic expressions.

Solutions and Values

• A zero of a function occurs at point x where f(x) = 0, indicating the x-intercepts of the graph.
• The roots of an equation are values that satisfy the equation.

Transformation Techniques

• Completing the square involves adding a term to create a perfect square trinomial, facilitating easier graphing and analysis.

Imaginary and Complex Numbers

• The imaginary unit i equals √(-1), a fundamental concept in complex numbers.
• Imaginary numbers are defined as the square roots of negative numbers.
• A complex number is expressed in the form a + bi, where a is the real part and b is the imaginary part.

The Complex Plane

• Real part refers to complex numbers where b = 0, while the imaginary part consists of numbers where a = 0 and b ≠ 0.
• The complex conjugate of a + bi is a - bi, an important relationship in complex number operations.
• The complex plane represents real numbers on the horizontal axis and imaginary numbers on the vertical axis.

Quadratic Inequalities and Applications

• A quadratic inequality in two variables features real numbers a, b, and c, with a ≠ 0.
• The discriminant within the Quadratic Formula helps ascertain the number of real roots for a quadratic equation.
• Quadratic regression is a technique for generating a quadratic model based on a data set, useful in statistical analysis.
• A quadratic model is essentially a quadratic function that accurately reflects a given data set.