Solving Quadratic Inequalities: Using Graphs and Discriminants

The video tutorial covers the basics of inequalities, focusing on symbols and their meanings. It explains how to solve quadratic inequalities using graphs, emphasizing the importance of sketching to find the range of values. Advanced techniques are introduced, including factorization and the use of the discriminant to determine the number of roots. The tutorial concludes with a summary of key points, reinforcing the importance of understanding inequality symbols and graph sketching.

What does a solid line in a graph of an inequality indicate?

• The values are not included.

• The values are included.

• The inequality is strict.

• The inequality is undefined.

In the inequality x^2 ≤ 16, what is the range of x values?

• x is between -4 and 4, exclusive.

• x is less than -4.

• x is greater than 4.

• x is between -4 and 4, inclusive.

When solving 5x^2 > 45, what is the first step?

• Multiply both sides by 5.

• Subtract 5 from both sides.

• Add 5 to both sides.

• Divide both sides by 5.

For the inequality x^2 > 9, what is the range of x values?

• x is greater than -3 and less than 3.

• x is exactly 3.

• x is less than -3 or greater than 3.

• x is between -3 and 3.

What is the purpose of factorizing a quadratic equation when solving inequalities?

• To find the roots.

• To determine the slope.

• To simplify the equation.

• To find the y-intercept.

In a negative quadratic inequality, what shape does the graph take?

• U-shaped curve.

• N-shaped curve.

• Circular shape.

• Straight line.

What does the discriminant tell us about a quadratic equation?

• The slope of the graph.

• The number of real roots.

• The y-intercept.

• The maximum value.

If the discriminant is zero, how many real roots does the quadratic equation have?

• Two roots.

• One root.

• No roots.

• Infinite roots.

What is the inequality for a quadratic equation with no real roots?

• Discriminant is greater than zero.

• Discriminant is less than zero.

• Discriminant is equal to zero.

• Discriminant is not defined.

How do you determine the range of values for a parameter in a quadratic equation using the discriminant?

• By ignoring the discriminant.

• By setting the discriminant less than zero.

• By setting the discriminant greater than zero.

• By setting the discriminant equal to zero.