5'7 Curve Fitting With Quadratic Models

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5.7 Curve Fitting With Quadratic Models
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Essential Question How can I write a quadratic
equation when given 3 coordinate
pairs? Objectives Find a quadratic function
that exactly fits three data points. Find a
quadratic model to represent a data set.
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Key Skills Find a quadratic function that
exactly fits three data points. Use a graphics
calculator to find a quadratic function whose
graph contains the points (21, 2), (22, 2), and
(1, 8).
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Solve a system of equations in order to find a
quadratic model that fits each set of data points
exactly.
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The table gives carbon monoxide (CO) emissions in
the United States for several years from 1940 to
1990. Emissions are measured in millions of tons.
Make a scatter plot of the data, using 1940 as
year 0. Find a quadratic regression equation for
the data. Use the equation to predict the amount
of carbon monoxide emitted in 2000.
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The model predicts about 92.7 million tons of CO
emissions in the year 2000.
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Lynda dives off the high diving board. You and
Carlo use a stopwatch and observe markings on the
side of the board to calculate Lyndas height
above the water at various times. As Carlo clocks
times of 0.5 seconds, 1 second, 1.5 seconds, and
2 seconds, you estimate Lyndas altitude as 24
meters, 25 meters, 22 meters, and 17 meters
respectively. Find the quadratic regression
equation that best fits these data.
Graph the data points and the regression equation.
Notice that the data do not exactly fit the
curve, but your estimates of height were actually
quite accurate.
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