Graph of the quadratic function f(x)=‒(x+4)(x‒6) is shown on the coordinate grid below. which statement is not true? a. the maximum of this function occurs when y=25. b. the function increases in the interval 1 to 6. c. the has a zero at (‒4,0). d. the function positive in the interval ‒4 to 6.

Option B is not true.

Step-by-step explanation:

The quadratic function is f(x) = -(x + 4)(x - 6)

Now we check each option given

Option A.

It is clear from the graph function is maximum at y = 25.

TRUE.

Option B.

Function increases in the interval 1 to 6.

Let's check this at x = 2 and x = 3

f(2) = -(2 + 4)(2 - 6)

     = -(6)(-4)

     = 24

f(3) = -(3 + 4)(3 - 6)

     = - (7)(-3)

     = 21

So we find this function is decreasing in this interval.

So the given option is FALSE.

Option C.

The function has a zero at (-4, 0)

f(-4) = -(-4 + 4)(-4 + 6) = 0

So the function has a zero at (-4, 0).

Option is True.

Option D.

The function is positive in the interval -4 to 6

f(x) = -(x + 4)(x - 6)

f(-3) = -(-3 + 4)(-3 - 6)

      = -(1)(-9)

      = 9

f(0) = -(0 + 4)( 0 - 6)

     = 24

Therefore, this function is positive in this interval so the option is TRUE.

Option B is not true.

x= -3 and

step-by-step explanation:

to find the roots of a cubic, use division or factoring to find the factors then set equal to 0. as this is a difference of cubes, it factors into

where a is the cube root of .

here   this is 27 and the cube root of 27 is 3. so we write using the form:

.

set each factor to 0 and solve for x.

x-3=0

x=3

the quadratic expression does not factor and must be solved using the quadratic formula.

where a = 1, b=3, and c=9

this cubic has two complex roots.