Quadratic Modeling and Regression 1. Write a quadratic in standard form of each graph. Use your calculator. a. b. c.

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d) Write a quadratic that passes through (1, -2), (-2, 1), (3, 6) 2. The table below lists temperatures measured in Farenheit and Celcius. A) Would linear or quadratic modeling be best in this situation?

B) Find a regression equation that models the data. Plug into Y = and sketch/label the scatter plot and the regression line.

C) Determine the equivalent temperature in Celsius degrees for a body temperature of 98.6 degrees Farenheit.

3. A study compared the speed s (in miles per hour) and the average fuel economy F(s) (in miles per gallon) for a certain make and model car. The results are shown in the table. A) Would linear or quadratic modeling be best in this situation?

B) Find a regression equation that models the data. Plug into Y = and sketch.

C) What speed will maximize fuel economy for this car?

4. Researchers compared protein intake to average shoulder and kidney weight for a group of pigs. The results are shown in the table. A) Write a quadratic model for the shoulder weight s and another for the kidney weight k as a function of the protein intake p.

B) Predict the shoulder weight and kidney weight of a pig with an average intake of 306 grams per day of protein.

C) What is the maximum shoulder weight? What protein intake is required to reach the maximum shoulder weight?

5. Two points on the parabolic path of a kicked football are (0, 0) and the vertex (20, 15). Write a quadratic function that models the path. Hint: find a third point!

6. In a track and field event, a contestant had a throw in the shot put that can be modeled by y = - 0.02x2 + x + 6 where x is the shot put’s horizontal distance (in feet) and y is the corresponding height (in feet). How long was the throw? Sketch the graph.

7. An object is launched upward with an initial velocity of 64 feet per second from a platform 80 feet high. The height h as a function of time t can be modeled by the equation ℎ(𝑡) = −16𝑡 2 + 𝑣0 𝑡 + ℎ0 where 𝑣0 is the initial velocity and ℎ0 is the initial height. A) Write a model for the object. B) How many seconds until the maximum height is reached?

C) What will be maximum height?

D) How many seconds until the object hits the ground?

SKETCH A GRAPH AND LABEL EACH ANSWER