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
Answers
Answer:
The value of 'y' when x = -4 is 2.3
Step-by-step 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).
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P:
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☆*: .｡..｡.:*☆☆*: .｡..｡.:*☆☆*: .｡..｡.:*☆☆*: .｡..｡.:*☆
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Step-by-step explanation:
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