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The graph of the function f(x) = -(x+6)(x + 2) is shown below. 46 £ Mark this and return 6+ 4 2 1-2- 4 2 ++ 4 6 X Which statement about the function is true? The function is increasing for all real values of x where O The function is increasing for all real values of x where -6 < x < -2. O The function is decreasing for all real values of x where x -2. O The function is decreasing for all real values of x where X​

Respuesta :

The correct statements regarding the behavior of a quadratic function are:

  • The function in increasing for all real values of x where -6 < x < -2.
  • The function is decreasing for all real values of x where x < -6 or x > -2.

When is a quadratic function increasing or decreasing?

A quadratic function with roots [tex]x_1[/tex] and [tex]x_2[/tex] is defined by:

[tex]y = a(x - x_1)(x - x_2)[/tex]

In which a is the leading coefficient.

The coefficient influences the behavior, as follows:

  • If a < 0, the function is increasing between the roots, and decreasing otherwise.
  • If a > 0, the function is decreasing between the roots, and increasing otherwise.

In this problem, the function is:

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

The roots are x = -6 and x = -2, and the leading coefficient is of a = -1 < 0, hence:

  • The function in increasing for all real values of x where -6 < x < -2.
  • The function is decreasing for all real values of x where x < -6 or x > -2.

More can be learned about quadratic functions at https://brainly.com/question/24737967

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