The Shot Put

The path of the winning throw in the Men’s 2000 Olympics can be modeled by the following Equation:

6015545.0 2 xxH

Graph the equation on your calculator.

• What is the practical domain?

• What is the practical range?

6015545.0 2 xxH

Use your calculator to complete the following table.

x 10 20 30 40 50

H

Estimate the coordinates of the vertex.

6015545.0 2 xxH

Finding the vertex.

• The vertex is the turning point of a parabola

( use )

The vertex can be found using these equations for the coordinate.

cbxaxy 2

a

acb

a

b

4

4,

2

2

Find the Vertex. 6015545.0 2 xxH

Finding the Maximum/Minimum.

6015545.0 2 xxH

Finding the Axes of Symmetry.

a

bx

2

Finding the intercepts of the parabola.

• Y-intercept (0,c)

When x = o then y = c.

• X-intercept when y = 0 then solve for x (*note you may have two answers)

Or use your calculator zero menu.

cbxaxy 2

Per Capita Personal Income

According to statistics from the US Department of Commerce, the per capita personal income (or the average annual income) of each resident of the United States from

1960 to 2000 can be modeled by …

where p represents the per capita income and t the number of years since 1960.

6909.18317687.981442.15 2 ttP

Use your calculator to complete the following table.

Year 1960 1965 1970 1975 1980 1985 1990 1995 2000

t

P(t)

What is the practical domain?

6909.18317687.981442.15 2 ttP

Estimate the per capita personal income in the year 1989 (t=29).

Determine the year in which the per capita income reached $20,500.

Ups and DownsSuppose a soccer goalie punted

the ball in such a way as to kick the ball as far as possible down the field. The height of the ball above the field as a function of time can be approximated by…

Where y represents the height of the ball (in yards) and x represents the horizontal distance down the field from where the goalie kicked the ball,

33.098.0017.0 2 xxy

33.098.0017.0 2 xxy

Use the graph to estimate how far downfield from the point of contact the soccer ball is 10 yards above the ground.

Enter 10 in y= in your calculator to find value of x.There are two answers.

Air Quality in AtlantaThe Air Quality Index (AQI) measures how polluted the air is by measuring five major pollutants:

• ground-level ozone• particulate matter• carbon monoxide• sulfur dioxide• nitrogen oxide

Based on the amount of each pollutant in the air, the AQI assigns a numerical value to air quality.

Air Quality Index0-50 Good

51-100 Moderate

101-150 Unhealthy for sensitive people

151-200 Unhealthy

201-300 Very Unhealthy

301-500 Hazardous

The following table indicates the number of days in which the AQI was greater than 100 in the city of Atlanta, Georgia.

Year 1990 1992 1994 1996 1998 1999

t (years since 1990) 0 2 4 6 8 9

Number of days

AQI > 100, n

42 20 15 25 50 61

Use your calculator to graph data.

Does it appear to be Quadratic?

Find the Quadratic Regression function.

Use the regression model to answer the following questions:

Estimate the year when the number of days the AQI exceeded 100 in Atlanta was 17.

Estimate the number of days the AQI exceeded 100 in Atlanta in 1995.