Answer:
A)<em> g(x) </em>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 <em>a</em> 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)<em> g(x) </em>has a greater absolute maximum.
