Algebra 2/Trig Chapter 2 Study Guide

Questions and Answers

What is the vertex form of a quadratic equation?

y = a(x + h)^2 + k

y = a(x - h)^2 + k (correct)

y = (x + h)(x - k)

y = ax^2 + bx + c

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

What is the standard form of a quadratic equation?

y = (x + p)(x + q)

y = ax + b

y = a(x - h)^2 + k

y = ax^2 + bx + c (correct)

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

Y scale, vertical stretch or shrink Signup and view all the answers

What is the zero of the function?

Value of the input that makes the output f(x) equal zero Signup and view all the answers

What is the process of completing the square?

x^2 + #x + (#/2)^2 = (x + #/2)^2 Signup and view all the answers

What is the quadratic formula?

X = -b ± √(b^2 - 4ac) / 2a Signup and view all the answers

What does the discriminant represent?

B^2 - 4ac Signup and view all the answers

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

True Signup and view all the answers

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

True Signup and view all the answers

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

False Signup and view all the answers

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

Two distinct non-real complex solutions Signup and view all the answers

What does the term 'SANDWHICH' refer to?

x^2 Signup and view all the answers

Study Notes

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.

Description

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.