Question

Complete each sentence with minimum or maximum and the corresponding numeric values.

The
value of f(x) = –|x – 4| – 5 is
when x =
.

The
value of f(x) = x2 – 2x +­ 1 is
when x =
.

Answer 1

First problem: max when x = 4

Second problem: min when x = 1

Explanation:

The graph of f(x) = –|x – 4| – 5 is a translation of that of g(x) = -|x|. The vertex of the latter is (0, 0). First this must be translated 4 units to the right and then the resulting graph 5 units downward. The vertex of this translation is (4, -5). Since this graph opens downward, this (4, -5) is the maximum function value, that is, when x = 4.

The graph of f(x) = x2 – 2x +­ 1, or (better yet) f(x) = x^2 – 2x +­ 1, or

f(x) = (x - 1)^2 + 0, is that of a parabola that opens upward and has its minimum at x = 1, or (1, 0).