Solving Quadratic Inequalities by Graphing and Factoring

The video tutorial explains how to solve quadratic inequalities, focusing on examples like X^2 > 9, X^2 ≤ 25, and 3X^2 ≥ 48. It covers both positive and negative values, highlights the importance of graphing, and introduces factorization techniques. The tutorial emphasizes understanding the structure of equations and inequalities, using graphical methods to find solutions, and practicing with examples to master the topic.

What is the first step in solving the inequality X^2 > 9?

• Graph the inequality directly.

• Test values of X to see when the inequality holds.

• Factorize the inequality.

• Use the quadratic formula.

When considering negative values of X for the inequality X^2 > 9, what is the tipping point?

• X = -2

• X = -1

• X = -3

• X = -4

In the graph of X^2 > 9, where does the graph of X^2 intersect the line y = 9?

• At X = 4 and X = -4

• At X = 3 and X = -3

• At X = 5 and X = -5

• At X = 0 and X = 9

For the inequality X^2 ≤ 25, what is the solution range?

• X is between -5 and 5

• X is between -4 and 4

• X is between -6 and 6

• X is between -3 and 3

What is the first step in solving a quadratic inequality using factorization?

• Graph the inequality.

• Convert the inequality to an equation.

• Use the quadratic formula.

• Test values of X.

When factorizing X^2 + 5X + 6, what are the roots?

• X = -1 and X = -6

• X = 1 and X = 6

• X = 2 and X = 3

• X = -2 and X = -3

How do you determine the shape of the parabola when sketching a quadratic inequality?

• By the roots of the equation.

• By the coefficient of X^2.

• By the coefficient of X.

• By the sign of the constant term.

What is the solution to the inequality 3X^2 > 48 after dividing by 3?

• X^2 > 16

• X^2 > 12

• X^2 > 24

• X^2 > 8

In the inequality -X^2 + X + 12 > 0, what is the shape of the parabola?

• Positive parabola

• Horizontal line

• Vertical line

• Negative parabola

What is the solution range for the inequality -X^2 + X + 12 > 0?

• X is between -3 and 4

• X is between -4 and 3

• X is between -5 and 2

• X is between -2 and 5