Quadratic Inequalities and Their Solutions

The video tutorial explains how to solve a quadratic inequality using interval notation. It begins by converting the inequality into standard form and finding critical points using the quadratic formula. The critical points are plotted on a number line, and test values are used to determine which intervals satisfy the inequality. The solution is verified graphically by examining the related quadratic function's graph.

What is the first step in solving a quadratic inequality?

• Finding the vertex

• Using the quadratic formula

• Rewriting it in standard form

• Graphing the inequality

What is the standard form of the given quadratic inequality?

• 3x^2 - 6x + 15 ≤ 0

• 3x^2 - 6x - 15 ≤ 0

• 3x^2 + 6x + 15 ≤ 0

• 3x^2 + 6x - 15 ≤ 0

Which method is used to find the critical points when the quadratic is not factorable?

• Synthetic division

• Graphing

• Completing the square

• Quadratic formula

What are the critical points of the inequality 3x^2 + 6x - 15 = 0?

• x = 1 ± √6

• x = -1 ± √6

• x = 2 ± √6

• x = -2 ± √6

How are critical points plotted on a number line for a 'less than or equal to' inequality?

• As open points

• As closed points

• As arrows

• As dashed lines

What test value is used for the interval to the left of the critical points?

• x = -4

• x = 0

• x = 2

• x = -3

Which interval is marked as true after testing x = 0?

• Middle interval

• Left interval

• None

• Right interval

What is the result of testing x = 2 in the inequality?

• Both true and false

• False

• Undefined

• True

What does the graph of the quadratic function help verify?

• The solution set of the inequality

• The axis of symmetry

• The vertex of the function

• The maximum value

What is the solution set of the inequality in interval notation?

• (-∞, -1 + √6] ∪ [-1 - √6, ∞)

• (-∞, -1 - √6] ∪ [-1 + √6, ∞)

• [-1 - √6, -1 + √6]

• [-1 + √6, -1 - √6]