Solving Equations and Inequalities through Graphing

The video tutorial covers solving equations and inequalities by graphing. It introduces tools like Desmos and graphing calculators to assist in graphing. Through examples, it demonstrates solving equations, absolute value equations, and inequalities using graphs. The tutorial also explains using tables to find intersection points, emphasizing the use of technology for ease and accuracy.

What is the essential question of this lesson?

• How can you solve an equation or inequality by graphing?

• What are the different types of equations?

• How do you solve equations by substitution?

• What is the importance of inequalities?

Which tool is NOT mentioned as an option for graphing?

• Desmos

• Graphing calculator

• Calculate 84 app

• Microsoft Excel

In Example 1, what is the solution to the equation when solved by graphing?

• x = 3

• x = -5

• x = 5

• x = -3

How do you split the equation in Example 1 for graphing?

• y = -3x - 20 and y = -5

• y = 3x - 20 and y = -5

• y = -3x + 20 and y = 5

• y = 3x + 20 and y = 5

What shape does the graph of an absolute value function form?

• A parabola

• A line

• A circle

• A V shape

In Example 2, what are the solutions to the absolute value equation?

• x = -2 and x = 10

• x = 2 and x = 10

• x = 2 and x = -10

• x = -2 and x = -10

What is the interval notation for the solution of the inequality in Example 3?

• (-∞, -2) ∪ (-2, 2)

• (-2, ∞) ∪ (2, ∞)

• (-∞, 2) ∪ (-2, ∞)

• (-∞, -2) ∪ (2, ∞)

How do you write the solution of the inequality in Example 3 as an inequality?

• x ≥ -2 and x ≤ 2

• x ≤ -2 and x ≥ 2

• x < -2 and x > 2

• x > -2 and x < 2

What feature can you use on a graphing calculator to find intersection points?

• First trace

• Third trace

• Fourth trace

• Second trace

How can you adjust the x interval in the table feature of a graphing calculator?

• By changing the y interval

• By changing the x interval to 0.1

• By changing the y interval to 0.1

• By changing the x interval to 1