Quadratic Inequalities and Graphs

This video tutorial covers quadratic inequalities, focusing on graph shapes and solving techniques. It includes examples and exam-style questions to illustrate how to find critical values, sketch graphs, and solve inequalities. The tutorial emphasizes understanding the impact of the coefficient of x squared on the graph's shape and provides strategies for solving inequalities involving x squared.

What determines the shape of a quadratic graph?

• The coefficient of x squared

• The linear term

• The constant term

• The coefficient of x

In a positive quadratic graph, where is y greater than zero?

• For x between a and b

• For x greater than zero

• For x less than a or more than b

• For x equal to a and b

In a negative quadratic graph, where is y less than zero?

• For x equal to a and b

• For x less than a or more than b

• For x between a and b

• For x greater than zero

What is the first step in solving a quadratic inequality?

• Find the critical values

• Multiply by x squared

• Solve for y

• Sketch the graph

How do you determine the critical values of a quadratic equation?

• Set y equal to zero

• Set y less than zero

• Set x equal to zero

• Set y greater than zero

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

• N shape

• U shape

• V shape

• W shape

When solving a quadratic inequality, why might you multiply by x squared?

• To simplify the equation

• To change the inequality direction

• To keep the inequality direction the same

• To eliminate x

What is the solution for x in a quadratic inequality where y is less than zero?

• x is more than zero

• x is equal to a and b

• x is more than a and less than b

• x is less than a or more than b

What does it mean if a quadratic equation has no real roots?

• The discriminant is less than zero

• The discriminant is equal to zero

• The discriminant is greater than zero

• The discriminant is a complex number

Why is x not equal to 3 in a quadratic inequality?

• It makes the equation positive

• It makes the equation undefined

• It makes the equation negative

• It makes the equation zero