Testing Quadratic Inequalities Concepts

The video tutorial explains how to solve a quadratic inequality by first ensuring it is in standard form, then finding critical points by factoring the quadratic equation. It involves plotting these points on a number line and testing intervals to determine which are part of the solution. The solution is verified using a graph of the quadratic function, confirming the intervals where the function is less than or equal to zero.

What is the first step in solving a quadratic inequality?

• Graphing the equation

• Setting the inequality to zero

• Factoring the equation

• Finding the critical points

Which method is used to factor the quadratic equation in this tutorial?

• Completing the square

• Synthetic division

• Trial and error

• Using the quadratic formula

What are the critical points of the equation 3x^2 + 7x - 20 = 0?

• x = 0 and x = 20

• x = 3 and x = -7

• x = 5/3 and x = -4

• x = -5 and x = 4

How do you determine if a point on the number line is open or closed?

• By checking if the inequality is strict or non-strict

• By using the quadratic formula

• By solving the equation

• By graphing the function

What test value is used for the interval to the left of x = -4?

• x = 0

• x = 2

• x = -3

• x = -5

What is the result of testing x = 0 in the inequality?

• The interval is undefined

• The interval is partially true

• The interval is true

• The interval is false

What is the significance of a positive product when testing intervals?

• It indicates the interval is partially true

• It indicates the interval is undefined

• It indicates the interval is false

• It indicates the interval is true

What is the solution interval for the inequality 3x^2 + 7x - 20 ≤ 0?

• [-4, 5/3]

• (-∞, -4]

• (-∞, ∞)

• [5/3, ∞)

How is the solution verified using a graph?

• By checking the y-intercept of the graph

• By checking the slope of the graph

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

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

What does the graph confirm about the solution interval?

• The interval is correct

• The interval needs adjustment

• The interval is incorrect

• The interval is partially correct