Quadratic Inequalities and Their Solutions

The video tutorial explains how to solve quadratic inequalities by setting them in relation to zero, finding critical points, and testing regions on a number line. It covers solving factored inequalities, testing regions for shading, and writing final solutions using inequalities. The tutorial also demonstrates how to factor expressions and determine shaded regions based on the inequality signs.

What is the first step in solving a quadratic inequality?

• Graph the inequality

• Find the vertex of the parabola

• Solve for y

• Set the inequality in relation to zero

How do you determine the critical points of a quadratic inequality?

• By solving for y

• By finding where the factors equal zero

• By setting the inequality to one

• By graphing the inequality

What does an open circle on a number line indicate in inequalities?

• The point is included in the solution

• The point is not included in the solution

• The inequality is greater than or equal to

• The inequality is less than or equal to

When testing regions, what does a negative product indicate?

• The inequality is satisfied

• The region is not shaded

• The region is shaded

• The inequality is not satisfied

In a quadratic inequality, where do you shade if the test point does not satisfy the inequality?

• On the axis of symmetry

• On the vertex

• Outside the parabola

• Inside the parabola

What is the solution for x in the inequality x - 3 = 0?

• x = 0

• x = 3

• x = 1

• x = -3

How do you factor x^2 - 16?

• (x + 4)(x + 4)

• (x - 4)(x + 4)

• (x + 8)(x - 2)

• (x - 4)(x - 4)

What type of circle is used on a number line for 'less than or equal to' inequalities?

• Open circle

• Dashed circle

• Closed circle

• Solid circle

How is the solution for x written if it is between -4 and 4, inclusive?

• -4 < x < 4

• -4 ≤ x ≤ 4

• -4 > x > 4

• -4 ≥ x ≥ 4

What is the inequality solution for x if x is less than -4/3 or greater than 3?

• x ≤ -4/3 or x ≥ 3

• x > -4/3 and x < 3

• x ≥ -4/3 and x ≤ 3

• x < -4/3 or x > 3