What is the domain and range of a quadratic graph

The video tutorial explains the concepts of domain and range in mathematical functions, focusing on parabolas. It covers how to graph parabolas with minimum and maximum values, and discusses the domain as the set of all possible x-values and the range as the set of possible y-values. The tutorial also explores how these concepts apply to specific equations, emphasizing that the domain of parabolas is all real numbers unless constrained, while the range depends on the graph's orientation and vertex.

What is the primary focus when discussing the domain of a function?

• The minimum value of the function

• The maximum value of the function

• The set of all possible X values

• The set of all possible Y values

In the context of parabolas, what does the domain typically include?

• Only negative X values

• Only positive X values

• Only integer X values

• All real numbers

How is the range of a function determined?

• By the slope of the tangent

• By the number of roots

• By the direction and vertex of the graph

• By the set of all possible X values

For a parabola that opens upwards, what is the range?

• All real numbers

• Only positive numbers

• From the vertex to positive infinity

• From negative infinity to the vertex

What happens to the range of a parabola that opens downwards?

• It extends from negative infinity to the vertex

• It extends from the vertex to positive infinity

• It includes all real numbers

• It includes only positive numbers

How does adding a constraint affect the domain of a parabola?

• It limits the range to positive numbers

• It restricts the domain to a specific set of X values

• It changes the direction of the parabola

• It has no effect on the domain

Why can't the range of a parabola include negative numbers when squared?

• Because the domain is restricted

• Because squaring always results in positive numbers

• Because the graph opens upwards

• Because the vertex is at zero