The points (0,3),(1, 4) (2, 7) , and (3, 12) are on the graph of a function . Write an explicit function that can be used to represent the function .

Question

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Answer 1

The function is of the second degree - quadratic

f(x) = ax² + bx c

3 = a(0)² + b(0) + c

3 = c

4 = a(1)² + b(1) + 3

1 = a + b

7 = a(2)² + b(2) +

4 = 4a + 2b

2 = 2a + 2b from 1 = a + b

4 = 4a + 2b

2 = 2a

a = 1

b = 0

f(x) = x² + 3