Answer:
- ∞ < x < 2
Option 3
Explanation:
The given function is
This is the equation of a parabola in vertex form
The general vertex form equation is f(x) =a(x -h)² + k
where (h, k) is the vertex which can be either a maximum or minimum and a is a constant
If a is positive, the vertex is at a minimum and the parabola opens downward
If a is negative, the vertex is at a maximum and the parabola opens upward
Here a = 1 is positive
The vertex is (2, 3) and is a minimum
So for all values of x < 2, the parabola is decreasing and for all values of x > 2 the parabola is increasing (see figure)
x = 2 is the turning point for the parabola
therefore the values of x for which the function is decreasing is
- ∞ < x < 2