Question

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

Answer 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

Explanation:

Answer 2

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