Question

Two different functions are shown. Function A: Function B: y = (x + 3)2 + 5 Which statement best compares the two functions? The minimum of function A occurs 1 unit higher than the minimum of function B. The minimum of function A occurs 3 units higher than the minimum of function B. The minimum of function A occurs 5 units lower than the minimum of function B. The minimum of function A occurs 7 units lower than the minimum of function B.

Answer 1

The true statement is (d) The minimum of function A occurs 7 units lower than the minimum of function B.

How to determine the true statement?

From the graph of function A (see attachment), the minimum value is:

Minimum of A = -2

The equation of function B is given as:

y = (x + 3)² + 5

The vertex (i.e. minimum) of the above function

Vertex = (-3,5)

This means that:

Minimum of B = 5

By comparison, -2 is 7 units smaller than 5

Hence, the minimum of function A occurs 7 units lower than the minimum of function B.

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