Compare the function ƒ(x) = –x2 + 4x – 5 and the function g(x), whose graph is shown. Which function has a greater absolute maximum (vertex)? Question 4 options: A) g(x) B) g(x) and ƒ(x) have equal absolute maximums. C) ƒ(x) D) There isn't enough information given.

A) g(x) has a greater absolute maximum.

Step-by-step explanation:

Given graph of g(x) which is a Parabola

1. Opens downwards

2. The absolute maximum (vertex) is at around (3.5, 6)

i.e. value of absolute maximum is 6.

Another function:

Let us convert it to vertex form to find its vertex.

Taking - sign common:

Now, let us try to make it a whole square,

Writing 5 as 4+1:

Please refer to attached graph of f(x).

We know that, vertex form of a parabola is given as:

Comparing the equations we get:

a = -1 (Negative value of a means the parabola opens downwards)

h = 2, k = -1

Vertex of f(x) is at (2, -1) i.e. value of absolute maximum is -1

and

Vertex of g(x) is at (3.5, 6)

i.e. value of absolute maximum is 6.

Hence, correct answer is:

A) g(x) has a greater absolute maximum.

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