Methods for Solving Quadratic Inequalities

The video tutorial covers solving quadratic inequalities using four methods: graphical, algebraic, sine diagram, and shortcut. Each method is explained with examples, focusing on understanding the nature of quadratic expressions and their solutions. The graphical method involves plotting the function, the algebraic method uses factorization, the sine diagram method checks signs across intervals, and the shortcut method offers a quick solution for advanced learners.

What is the degree of a quadratic expression?

• 3

• 2

• 4

• 1

Which of the following is NOT a type of quadratic inequality?

• Less than or equal to

• Equal to

• Less than

• Greater than

How many methods are discussed for solving quadratic inequalities?

• Four

• Three

• Five

• Two

What is the first method discussed for solving quadratic inequalities?

• Graphical method

• Shortcut method

• Sine diagram method

• Algebraic method

In the graphical method, what does a positive leading coefficient indicate about the parabola?

• Horizontal

• Vertical

• Concave up

• Concave down

What is the solution set for the inequality x^2 - x - 2 < 0 using the graphical method?

• (-1, 2)

• (-∞, ∞)

• (2, ∞)

• (-∞, -1)

In the algebraic method, why is it important to consider two cases?

• To make it easier to graph

• To simplify calculations

• To ensure all solutions are found

• To avoid complex numbers

What is the result when both factors in the algebraic method are positive?

• Zero product

• Positive product

• Negative product

• Undefined product

Which method is described as the instructor's favorite?

• Sine diagram method

• Algebraic method

• Graphical method

• Shortcut method

What is the purpose of using test points in the sine diagram method?

• To find zeros

• To solve the inequality

• To graph the function

• To determine the sign of intervals