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.

Step-by-step explanation:

we have

This is a vertical parabola open upward

The vertex is a minimum

The vertex is the point (1.5,-6.25)

we know that

The function is decreasing in the interval ----> (-∞,1.5)  x < 1.5

That means----> the function is decreasing for all real values of x less than 1.5

The function is increasing in the interval ----> (1.5,∞)  x> 1.5

That means----> the function is increasing for all real values of x greater than 1.5

see the attached figure to better understand the problem

therefore

The statement that is true is

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

step-by-step explanation:

equation

you are asked to write the equation

  expression = 0

using the given expression. when you do that, you have

  2x^2-2x-12 = 0

factoring

you can see that each of the coefficients is even, so a factor of 2 can be removed immediately.

  2(x^2 -x -6) = 0

if you multiply the binomials (x+a)(x+b), you get

  (x +a)(x +b) = x^2 +(a+b)x +ab

this tells you the coefficient of x is the sum of two factors of the constant term. here, that means -1 is the sum of two factors of -6. we want to know those factors so we can factor the trinomial.

  -6 = -1×6 = -2×3 = -3×2 = -6×1

the factor pair that sums to -1 is {-3, 2}, so our factorization is

  2(x -3)(x +2) = 0

solutions

the solutions to this equation are the values of x that make the product zero. a product is zero only when only of the factors of the product is zero. here, that means

  x - 3 = 0

  x = 3 . . . add 3 to both sides of the equation

or

  x +2 = 0

  x = -2 . . . add -2 to both sides of the equation

the solutions to the equation are x=3 or x=-2. both of these values of x satisfy the equation—they make it be true.

show us the picture

step-by-step explanation:

show the !