Quadratic Inequalities and Interval Notation

The video tutorial explains how to solve quadratic inequalities using a step-by-step approach. It covers finding zeros of the related quadratic equation, plotting these on a number line, testing intervals, and graphing the solution. An example problem is solved by factoring, and the solution is verified graphically. The tutorial also explains how to express the solution using interval notation and inequalities.

What is the first step in solving a quadratic inequality?

• Graphing the inequality

• Finding the zeros of the related quadratic equation

• Testing values in each interval

• Stating the solution using interval notation

When solving a quadratic equation by factoring, what do the factors represent?

• The x-intercepts of the graph

• The maximum point of the parabola

• The y-intercepts of the graph

• The slope of the line

What does an open point on the number line indicate?

• The interval is false

• The interval is true

• The endpoint is not included in the solution

• The endpoint is included in the solution

How do you determine if an interval satisfies the inequality?

• By calculating the area under the curve

• By finding the derivative of the function

• By using a test value within the interval

• By checking if the interval is above the x-axis

Which test value would you use for the interval (-∞, -5)?

• x = -4

• x = -6

• x = 7

• x = 0

Which interval notation is used when endpoints are not included?

• Square brackets

• Curly braces

• Rounded parentheses

• Angle brackets

What is the solution to the inequality x^2 - x - 30 < 0 in interval notation?

• (5, 6)

• [-5, 6]

• (-5, 6)

• (-∞, -5) ∪ (6, ∞)

What is the purpose of using a compound inequality?

• To express the solution in a single statement

• To find the derivative of the function

• To calculate the area under the curve

• To determine the slope of the tangent line

How can the solution to a quadratic inequality be verified graphically?

• By checking where the graph is above the x-axis

• By checking where the graph is below the x-axis

• By finding the vertex of the parabola

• By determining the slope of the tangent line

What does it mean if the function values are below the x-axis?

• The function values are positive

• The function values are negative

• The function values are zero

• The function is increasing