Algebra 2/Trig Chapter 2 Study Guide

What is the vertex form of a quadratic equation?

What does X equal in the context of a quadratic function?

What is the standard form of a quadratic equation?

What does 'a' represent in the standard form of a quadratic equation?

What is the zero of the function?

What is the process of completing the square?

What is the quadratic formula?

What does the discriminant represent?

If b^2 - 4ac = 0, there is one distinct real solution.

If b^2 - 4ac > 0, there are two distinct real solutions.

If b^2 - 4ac < 0, there are two distinct real solutions.

What does the expression 'b^2 - 4ac < 0' represent?

What does the term 'SANDWHICH' refer to?

Vertex Form and Axis of Symmetry

The vertex form of a quadratic function is given by ( y = a(x-h)^2 + k ).
The vertex is represented by the point ( (h, k) ).
The axis of symmetry of the parabola is defined by the line ( x = h ).

Standard Form and Characteristics

The standard form of a quadratic function is ( y = ax^2 + bx + c ).
In this form, ( a ) determines the vertical stretch or shrink of the parabola. A positive ( a ) opens upwards, while a negative ( a ) opens downwards.

Zeros of the Function

The zeros of the function are the input values that make the output ( f(x) = 0 ).

Completing the Square

Completing the square involves rewriting a quadratic equation in the form ( x^2 + bx + (b/2)^2 = (x + b/2)^2 ).

Quadratic Formula

The quadratic formula to find the roots of a quadratic equation is given by ( x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} ).

Discriminant Analysis

The discriminant, represented by ( b^2 - 4ac ), determines the nature of the roots of the quadratic equation.
If ( b^2 - 4ac = 0 ), there is one distinct real solution.
If ( b^2 - 4ac > 0 ), there are two distinct real solutions.
If ( b^2 - 4ac < 0 ), there are two distinct non-real complex solutions.

General Notes

Always check the value of the discriminant to identify the types of solutions for quadratic equations.

This flashcard set covers key concepts from Algebra 2/Trig Chapter 2, including vertex form, axis of symmetry, and standard form of quadratic equations. Enhance your understanding of quadratic functions and their properties with these essential definitions.