Question

Compare the function represented by the table to the function represented by the graph to determine which statement is true.

A) The tabled function has a lower minimum value.

B) The tabled function has a greater maximum value.

C) The graphed function has a lower minimum value.

D) The graphed function has a greater maximum value.

Answer 1

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.