Question

The table shows the average sale price, p, of a house in a city, for various years, t, since 1980:312456oYears since 1980, t24362129212024Average Sale Price (in thousandsof dollars). p

Answer 1

1) Quadratic function

Step-by-step 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.

`slope=m\text{ = }(y_2-y_1)/(x_2-x_1)`

point (0, 36) and (1, 29)

`\text{slope = }\frac{29\text{ - 36}}{1-0}=(-7)/(1)\text{ = -7}`

point (1, 29) and (2, 24)

`\text{slope = }\frac{24\text{ - 29}}{2-1}=(-5)/(1)\text{ = -5}`

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.