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Sagot :
1) Quadratic function
Explanation:1) We need to find the slope or the rate. If it is constant for any two points, then it will be a linear function.
[tex]slope=m\text{ = }\frac{y_2-y_1}{x_2-x_1}[/tex]point (0, 36) and (1, 29)
[tex]\text{slope = }\frac{29\text{ - 36}}{1-0}=\frac{-7}{1}\text{ = -7}[/tex]point (1, 29) and (2, 24)
[tex]\text{slope = }\frac{24\text{ - 29}}{2-1}=\frac{-5}{1}\text{ = -5}[/tex]From the above we can see the slope is not constant. Hence, it is not a linear function
For a quadratic function, we check for the 2nd difference. If it is constant then it is quadratic.
First difference = change in y values (change in price)
First difference = -7, -5, -3, -1
Second difference:
-5 - (-7) = -5 + 7 = 2
-3 - (-5) = -3 + 5 = 2
-1 - (-3) = -1 + 3 = 2
The second difference for the points is the same. Hence,the function that most appropraitely represents this data is a quadratic function.
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