Question

The graph of the function f(x) = -(x+6)(x + 2) is shown

below.
Which statement about the function is true?
The function is increasing for all real values of x where
x< 4.
The function is increasing for all real values of x where
-6 The function is decreasing for all real values of x where
X<-6 and where x > -2.
The function is decreasing for all real values of x where
x< 4.
+6
-4
HHHHH
2 4 6
x

Answer 1

The function is increasing for all real values of x where

x< 4.

Explanation:

edge 2021

For an explanation look above^

Answer 2

The function is increasing for all real values of x where

x < –4.

Explanation:

we have

`f(x)=-(x+6)(x+2)`

This is a vertical parabola open downward (the leading coefficient is negative)

The vertex (h,k) represent a maximum

The roots of the function (or x-intercepts) are x=-6 and x=-2

The x-coordinate of the vertex is the midpoint of the roots

so

`h=(-2-6)/2=-4`

The y-coordinate of the vertex is

substitute the x-coordinate of the vertex in the quadratic equation

`k=-(-4+6)(-4+2)`

`k=-(2)(-2)`

`k=4`

The vertex is the point (-4,4)

The function is increasing in the interval (-∞,-4)

The function is decreasing in the interval (-4,∞)