The graph of the function f(x) = (x – 4)(x + 1) is shown below.

on a coordinate plane, a parabola opens up. it goes through (negative 1, 0), has a vertex at (1.75, negative 6.2), and goes through (4, 0).

which statement about the function is true?

the function is increasing for all real values of x where
x < 0.
the function is increasing for all real values of x where
x < –1 and where x > 4.
the function is decreasing for all real values of x where
–1 < x < 4.
the function is decreasing for all real values of x where
x < 1.5.

The function is decreasing for all real values of x where  x < 1.5 ⇒ 4th

Step-by-step explanation:

* Lets revise some points about the quadratic function

- The quadratic represented graphically by a parabola

- If the vertex of the parabola is point (h , k), then

- Point (h , k) is the minimum point of the function if the parabola opens

   upward

- Point (h , k) is the maximum point of the function if the parabola opens

   downward

- If point (h , k) is a minimum point, then the function is decreasing

  for all values of x smaller than h and increasing for all values of x

  greater than h

- If point (h , k) is a maximum point, then the function is increasing for

   all values of x smaller than h and decreasing for all values of x greater

   than h

* Now lets solve the problem

- From the attached graph and the given

∵ The parabola represents a quadratic function

∵ The parabola opens upward

∴ Its vertex is minimum

- Lets use the bold point above

∵ The coordinates of the vertex are (1.75 , -6.2)

∴ The function is decreasing for all values of x less than 1.75

* The function is decreasing for all real vales of x where x < 1.75

∴ The function is increasing for all values of x greater than 1.75

* The function is increasing for all real vales of x where x > 1.75

- From the answer there is only one statement true

- The statement is:

  The function is decreasing for all real values of x where  x < 1.5,

   because the function is decreasing for all real values of x where

    x < 1.75 and 1.5 is smaller than 1.75

* The function is decreasing for all real values of x where  x < 1.5