Answer:
Option (C)
Explanation:
Let the quadratic function representing table is,
f(x) = ax² + bx + c
From the given table,
For x = 2, y = 6
a(2)² + b(2) + c = 6
4a + 2b + c = 6 --------(1)
For x = 3, f(x) = 11
a(3)² + 3b + c = 11
9a + 3b + c = 11 ------(2)
For x = 4, f(x) = 18
a(4)² + b(4) + c = 18
16a + 4b + c = 18 ------- (3)
Equation (1) - Equation (2)
(4a + 2b + c) - (9a + 3b + c) = 6 - 11
-5a - b = -5
5a + b = 5 -----(4)
Equation (2) - equation (3)
7a + b = 7 -----(5)
Equation ( 5) - equation (4)
(7a + b) - (5a + b) = 7 - 5
2a = 2 ⇒ a = 1
From equation (4),
5 + b = 5 ⇒ b = 0
From equation (1),
4(1) + 0 + c = 6
c = 2
Therefore, quadratic function is,
f(x) = x²+ 2
f(x) = (x - 0)² + 2
Vertex of the function will be → (0, 2).
Vertex of the graph given in the picture → (0.5, -0.2)
By comparing both the vertices,
Minimum value of the graphed function = -0.2
Minimum value of the function given in the table = 2
Graphed function has the lower minimum value.
Option (C) will be the correct option.