Comprehensive Guide to Algebra 2: Solving Equations and Graphing

Created from Youtube video: https://www.youtube.com/watch?v=i6sbjtJjJ-Avideo

Concepts covered:Algebra 2, linear equations, quadratic equations, graphing inequalities, factoring

This video provides a comprehensive overview of basic Algebra 2 concepts, including solving linear equations, graphing inequalities, and factoring quadratic equations. It also covers methods for solving systems of equations and graphing quadratic functions in both vertex and standard forms.

Table of Contents1.Solving Absolute Value Equations and Inequalities 2.Graphing Linear Equations: Slope-Intercept and Standard Forms 3.Graphing Linear Inequalities 4.Graphing Inequalities: Shading and Line Types 5.Transformations of Absolute Value Functions

chapter

Solving Absolute Value Equations and Inequalities

Concepts covered:absolute value, inequalities, equation manipulation, interval notation, number line

The chapter explains how to solve absolute value equations and inequalities by manipulating the equation to isolate the absolute value expression. It demonstrates the process through examples, emphasizing the importance of changing the inequality sign when multiplying or dividing by a negative number.

Question 1

Dividing by a negative number changes inequality direction.

Question 2

Why must you change the inequality sign when dividing by a negative?

Question 3

Where is 13/2 located on a number line?

Question 4

CASE STUDY: You need to solve the inequality |3x + 2| ≥ 8 and find the solution set.

All of the following are correct steps except:

Question 5

CASE STUDY: Given the inequality |2x - 7| ≤ 5, solve for x and plot the solution.

Select three correct steps out of the following:

chapter

Graphing Linear Equations: Slope-Intercept and Standard Forms

Concepts covered:slope-intercept form, standard form, graphing, linear equations, intercepts

This chapter explains how to graph linear equations in both slope-intercept form and standard form. It provides step-by-step instructions for plotting points and drawing lines based on the slope and intercepts of the equations.

Question 6

The slope of y = 2x - 3 is 2.

Question 7

How do you graph 3x + 4y = 12?

Question 8

How do you find the x-intercept in standard form?

Question 9

CASE STUDY: A company wants to visualize their sales data over time. They have the equation y = 5x + 10, where y represents sales and x represents time in months.

All of the following are correct applications of graphing the sales data except...

Question 10

CASE STUDY: An engineer is analyzing the stress on a beam using the linear equation 3x - 2y = 6. They need to graph this equation.

Select three correct steps to graph this equation.

chapter

Graphing Linear Inequalities

Concepts covered:linear inequality, slope-intercept form, dashed line, shading region, test point

The chapter explains how to graph a linear inequality, specifically when y is less than 3x plus 1. It covers identifying the slope and y-intercept, plotting points, using a dashed line for the inequality, and shading the correct region of the graph.

Question 11

A solid line is used for y < 3x + 1.

Question 12

What is the next point after (1, 4) for y < 3x + 1?

Question 13

What type of line is used for y < 3x + 1?

Question 14

CASE STUDY: You are tasked with graphing the inequality y > 2x - 4. You identify the slope and y-intercept and plot the points accordingly.

All of the following are correct steps except:

Question 15

CASE STUDY: In your homework, you need to graph the inequality y ≥ 4x - 2. You have identified the slope and y-intercept.

Select three correct steps out of the following:

chapter

Graphing Inequalities: Shading and Line Types

Concepts covered:inequalities, graph shading, slope, y-intercept, testing points

The chapter explains how to determine the appropriate region to shade on a graph based on inequalities. It covers the process of testing points, understanding the slope and y-intercept, and deciding whether to use a solid or dashed line.

Question 16

A solid line is used for y ≥ 2x + 5.

Question 17

What is the slope in the given problem?

Question 18

Where is the next point from (0,5) with slope -2?

Question 19

CASE STUDY: You are plotting a graph with the equation y ≥ -2x + 5. You need to determine the appropriate region to shade on the graph.

All of the following points should be shaded except:

Question 20

CASE STUDY: You need to determine the slope and y-intercept for the equation y ≥ -2x + 5.

Select three correct characteristics of the equation:

chapter

Transformations of Absolute Value Functions

Concepts covered:absolute value, graph transformations, shifting, reflecting, translating

The chapter discusses the transformations of absolute value functions and their graphical representations. It explains how shifting, reflecting, and translating the graph affects its shape and position on the coordinate plane.

Question 21

Negative sign outside absolute value reflects graph over x-axis.

Question 22

Where does the graph of |x-3|+2 shift?

Question 23

What happens when a negative sign is outside the absolute value?

Question 24

CASE STUDY: A company is modeling its profit using the absolute value function P(x) = |x - 5| - 2. They want to understand how changes in the function affect the graph.

All of the following are correct transformations except:

Question 25

CASE STUDY: A student is graphing the function f(x) = |x - 1| + 4 for a math project. They need to identify the key transformations.

Select three correct transformations out of the following:

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