# (1 & 2)

The first three points do not fall on a straight line, and there is no value of k that will make that happen.

(4) To find the quadratic

y = a x^2 + bx + c

that passes through the first three points, solve simultaneously

1 = c

3 = 4a + 2b + c

6 = 16 a + 4b + c

2 = 4a + 2b

5 = 16 a + 4b

4 = 8a + 4b

8a = 1

a = 1/8

2 = 1/2 + 2b

b = 3/4

y = (1/8)x^2 + (3/4)x + 1

Given ordered pairs (0,1),(2,3),(4,6),(6,k), answer the following questions

1. Determine a value for k so data points follow a linear model.

2. Find the linear model(equation).

3. Determine a value for k so data points follow a quadratic model.

4. Find the quadratic model(equation).