Identify the quadratic function that contains the points (-1,1), (0,-2) and (2,4). f(x) = 2x2 + x + 1

The general equation of the quadratic function is:

f(x) = ax² + bx + c
the quadratic function contains the points (-1,1), (0,-2) and (2,4)

by substitution with each point to make a system of equations to find a, b and c

substitution with (-1,1) ⇒⇒⇒    1 = a - b + c          → (1)
substitution with (0,-2) ⇒⇒⇒    -2 = c                    → (2)
substitution with (2,4)  ⇒⇒⇒     4 = 4a + 2b + c     → (3)

solving the equations (1), (2) and (3)

∴ a = 2  ,   b = -1   ,   c = -2


∴ The quadratic function that contains the points (-1,1), (0,-2) and (2,4)
 is f(x) = 2x² - x - 2