Solving Quadratic Inequalities

What is the primary difference between a quadratic equation and a quadratic inequality?

• Quadratic inequalities do not involve variables.

• Quadratic equations do not have solutions.

• Quadratic inequalities can only have positive solutions.

• The presence of an equal sign in equations versus an inequality sign in inequalities.

What are critical values in the context of solving quadratic inequalities?

• Values that make the equation equal to zero.

• Values that make the inequality true for all x.

• The maximum and minimum points of the graph.

• The x-intercepts of the graph.

Tags

CCSS.HSA.APR.B.3

CCSS.HSA.REI.B.4

How do you determine the section of the graph where a quadratic inequality is true?

• By finding where the graph is above or below the x-axis.

• By calculating the slope of the graph.

• By locating the vertex of the graph.

• By identifying the y-intercept.

Tags

CCSS.HSA.CED.A.3

What is the purpose of case analysis (using a number line) in solving quadratic inequalities?

• To find the exact points where the graph crosses the x-axis.

• To avoid drawing graphs.

• To simplify the equation to x=0.

• To identify sections of the solution without graphing.

Tags

CCSS.HSA.CED.A.1

CCSS.HSA.CED.A.3

In case analysis, how do you test if a section is part of the solution?

• By calculating the area under the graph.

• By determining if the section contains the vertex.

• By checking if the graph crosses the x-axis in that section.

• By substituting a value from the section into the inequality.

Tags

CCSS.HSA.CED.A.3

CCSS.HSA.REI.D.11

CCSS.HSA.REI.D.12

When solving a quadratic inequality, why might you need to adjust the equation before factorizing?

• To set the right-hand side to zero.

• To simplify the equation to a linear form.

• To ensure the coefficient of x^2 is positive.

• To find the x-intercepts.

What is the primary difference between a quadratic equation and a quadratic inequality?

• Quadratic inequalities do not involve variables.

• Quadratic equations do not have solutions.

• Quadratic inequalities can only have positive solutions.

• The presence of an equal sign in equations versus an inequality sign in inequalities.

What are critical values in the context of solving quadratic inequalities?

• Values that make the equation equal to zero.

• Values that make the inequality true for all x.

• The maximum and minimum points of the graph.

• The x-intercepts of the graph.

How do you determine the section of the graph where a quadratic inequality is true?

• By finding where the graph is above or below the x-axis.

• By calculating the slope of the graph.

• By locating the vertex of the graph.

• By identifying the y-intercept.

Tags

CCSS.HSA.APR.B.3

CCSS.HSA.CED.A.3

What is the purpose of case analysis (using a number line) in solving quadratic inequalities?

• To find the exact points where the graph crosses the x-axis.

• To avoid drawing graphs.

• To simplify the equation to x=0.

• To identify sections of the solution without graphing.