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Determine the quadratic curve of best fit for the data. Then estimate what the value of will be when = −4. {(−3,2), (0,5), (1,7.3), (−1,3.3), (−6,5), (−7,7.3)} Answer choices 4.3 5.3 3.3 2.3

User DrChivas
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Answer:

The value of 'y' when x = -4 is 2.3

Explanation:

Curve of best fit can be found by plotting the points on MS Excel and drawing a curve that goes through the points as shown in the attached graph

The equation that approximate the curve from which the y-value at a x-value of -4 can be estimated is found as follows

The general equation for a quadratic equation is y = a·x² + b·x + c

Therefore, we get;

2 = a·(-3)² + b·(-3) + c

2 = 9·a - 3·b + c

5 = 0·a + 0·b + c

5 = c

7.3 = 1·a + 1·b + c = a + b + 5

7.3 = a + b + 5

2.3 = a + b

2 = 9·a - 3·b + 5

-3 = 9·a - 3·b

Solving gives;

a = 13/40, b = 79/40

The equation of the quadratic curve is therefore;

y = (13/40)·x² + (79/40)·x + 5

When x = -4, we get;

y = (13/40)·(-4)² + (79/40)·(-4) + 5 = 2.3

When x = -4, y = 2.3

Plotting the points on MS Excel we find from the attached graph that the estimated value of 'y' when x = -4 is as calculated (2.3).

Determine the quadratic curve of best fit for the data. Then estimate what the value-example-1
User Jason De Oliveira
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