Understanding Quadratic Functions and Unemployment Rates

The video tutorial explains how a quadratic function models the annual unemployment rate in the Phoenix-Mesa-Scottsdale area from 2008 to 2014. It demonstrates using a graphing method to determine when the unemployment rate was greater than 6.25% and less than 8.25%, using a TI-84 calculator to find points of intersection. The tutorial covers interval notation and the interpretation of results in terms of years.

What does the quadratic function u(t) represent in the context of the Phoenix-Mesa-Scottsdale area?

• The annual GDP growth rate

• The annual unemployment percentage rate

• The annual population growth rate

• The annual inflation rate

What is the domain of the quadratic function u(t) in terms of t?

• t is between 0 and 7, including both 0 and 7

• t is greater than 7

• t is less than 0

• t is between 0 and 7, including 0 but not 7

How do you determine when the unemployment rate was greater than 6.25% using a graph?

• By finding when the graph is parallel to the horizontal line

• By finding when the graph intersects the horizontal line

• By finding when the graph is above the horizontal line

• By finding when the graph is below the horizontal line

In interval notation, how is the period when the unemployment rate was above 6.25% expressed?

• (0, 5.5)

• [0, 5.5]

• (0, 5.5]

• [0, 5.5)

What tool is used to find the intersection points on the graph for the unemployment rate analysis?

• Excel spreadsheet

• TI-84 calculator

• Graphing paper

• Scientific calculator

During which years was the unemployment rate above 6.25%?

• 2008 to 2013

• 2009 to 2014

• 2008 to 2012

• 2009 to 2013

When analyzing the unemployment rate being less than 8.25%, what is the significance of the intersection points?

• They determine the minimum rate

• They are included in the interval

• They are excluded from the interval

• They determine the maximum rate

In interval notation, how is the period when the unemployment rate was below 8.25% expressed?

• [0, 1.2) ∪ (4.1, 7]

• [0, 1.2) ∪ (4.1, 7)

• (0, 1.2] ∪ [4.1, 7)

• (0, 1.2) ∪ (4.1, 7)

During which years was the unemployment rate below 8.25%?

• 2009 to 2010 and 2013 to 2015

• 2008 to 2010 and 2011 to 2013

• 2009 to 2011 and 2012 to 2014

• 2008 to 2009 and 2012 to 2014

What is the significance of using interval notation in this analysis?

• It helps in calculating the exact unemployment rate

• It determines the function's maximum value

• It provides a concise way to express the range of years

• It is used to find the average unemployment rate