Find coefficients a, b and c such that the graph of the function f(x) = ax^2 + bx + c passes through the points (0, −2),(1, 1) and (2, 3).

Question

Find coefficients a, b and c such that the graph of the function f(x) = ax² + bx + c passes through the points (0, −2),(1, 1) and (2, 3).

Answer 1

Since (0, -2) is on the graph, a(0)² + b(0) + c = -2. So, c = -2.

Since (1,1) is on the graph, a + b - 2 = 1

Since (2,3) is on the graph, 4a + 2b - 2 = 3

So, a + b = 3 and 4a + 2b = 5

Solve for a and b.