Exploring Domain and Range in Interval Notation

This video tutorial explains interval notation, a method for writing sets of numbers, focusing on its use with quadratics. It covers the symbols used in interval notation, such as parentheses and brackets, and demonstrates how to graph quadratics using vertex form. The video also explains how to determine the domain and range of a quadratic function in interval notation, using examples with both positive and negative leading coefficients. The tutorial concludes with a final example and a brief mention of future topics, including root functions and set builder notation.

What type of symbol is used in interval notation to represent an open value?

• Bracket

• Curly brace

• Parenthesis

• Square

In vertex form of a quadratic equation, what does the 'H' value represent?

• The y-intercept

• The slope

• The y-coordinate of the vertex

• The x-coordinate of the vertex

What is the domain of a quadratic function in interval notation?

• Negative infinity to positive infinity

• Zero to positive infinity

• Zero to one

• Negative infinity to zero

Why do we use parentheses for infinity in interval notation?

• Because infinity is a negative number

• Because infinity is a finite number

• Because infinity cannot be contained

• Because infinity is a closed value

What is the range of a quadratic function with a minimum y-value of 3?

• (3, infinity)

• (-infinity, 3]

• [3, infinity)

• (-infinity, 3)

What happens to the parabola when the 'a' value in the quadratic equation is negative?

• It opens upwards

• It shifts to the left

• It opens downwards

• It shifts to the right

What is the vertex of the quadratic function given by the equation (x + 5)^2 + 3?

• (-5, -3)

• (5, 3)

• (5, -3)

• (-5, 3)

In interval notation, how do you represent a range that includes the value 3 and extends to positive infinity?

• (3, infinity)

• [3, infinity)

• (3, infinity]

• [3, infinity]

What is the domain of the quadratic function (x + 5)^2 + 3?

• (-5, infinity)

• (-infinity, infinity)

• (-5, 5)

• (-infinity, 5)

What is the range of an upside-down parabola with a maximum y-value of -1?

• [-1, infinity)

• [-1, infinity]

• (-infinity, -1]

• (-infinity, -1)