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

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Presentation transcript:

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

Graph the equation on your calculator. What is the practical domain? What is the practical range?

Use your calculator to complete the following table. x H Estimate the coordinates of the vertex.

Finding the vertex. The vertex is the turning point of a parabola ( use ) The vertex can be found using these equations for the coordinate. Find the Vertex.

Finding the Maximum/Minimum.

Finding the Axes of Symmetry.

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.

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.

Use your calculator to complete the following table. Year t P(t) What is the practical domain? 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 Downs Suppose 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,

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 Atlanta The 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 Index 0-50Good Moderate Unhealthy for sensitive people Unhealthy Very Unhealthy Hazardous

The following table indicates the number of days in which the AQI was greater than 100 in the city of Atlanta, Georgia. Year t (years since 1990) Number of days AQI > 100, n 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.