Answer:
The function is negative for all real values of x where -6< x < -2
Step-by-step explanation:
Given f(x) = (x + 2)(x + 6)
The graph of the function is as shown in the attached figure.
As shown, we can deduce the following:
The function is positive for all real values of x where x > -2 and x < -6
The function is zero at x = -2 and x = -6
The function is negative for all real values of x where -6 < x <-2
Compare the observations to the given statements:
So, The true statement is The function is negative for all real values of x where -6 < x <-2
The maximum height is yo<span> = 0</span>
When the projectile is at its maximum height <span> v</span>y = 0.
Note that the maximum height is determined solely by the initial velocity in the y direction and the acceleration due to gravity. :)
the answer is in the picture I mentioned as the answer ok ◉‿◉◉‿◉◉‿◉◉‿◉◉‿◉◉‿◉◉‿◉◉‿◉◉‿◉◉‿◉◉‿◉◉‿◉◉‿◉◉‿◉◉‿◉◉‿◉◉‿◉◉‿◉
The x =0 and y = 1 are coordinates of point E, which partitions the directed line segment from A to B into a ratio of 1:2.
<h2>We have to determine</h2>
What are the x- and y- coordinates of point E, which partitions the directed line segment from A to B into a ratio of 1:2?
<h3>According to the question</h3>
A line segment at points A(2, -3) and B (-4, 9).
The x- and y- coordinates of point E, which partitions the directed line segment from A to B into a ratio of 1:2 is given by;
![\rm x=\dfrac{m}{(m+n)} [x_2- x_1]+ x_1 \\ \\ y=\dfrac{m}{(m+n)} [y_2- y_1]+ y_1 \\ \\](https://tex.z-dn.net/?f=%5Crm%20x%3D%5Cdfrac%7Bm%7D%7B%28m%2Bn%29%7D%20%5Bx_2-%20x_1%5D%2B%20x_1%20%5C%5C%0A%5C%5C%0A%20y%3D%5Cdfrac%7Bm%7D%7B%28m%2Bn%29%7D%20%5By_2-%20y_1%5D%2B%20y_1%20%5C%5C%0A%5C%5C)
Where 
Substitute all the values in the formula;
![\rm x=\dfrac{m}{(m+n)} [x_2- x_1]+ x_1 \\\\](https://tex.z-dn.net/?f=%5Crm%20x%3D%5Cdfrac%7Bm%7D%7B%28m%2Bn%29%7D%20%5Bx_2-%20x_1%5D%2B%20x_1%20%5C%5C%5C%5C%20)
![\rm x=\dfrac{1}{(1+2)} [-4-(2)]+ (2)\\\\ x = \dfrac{1}{3} \times (-6) +2 \\ \\ x = -2+2\\ \\ x=0](https://tex.z-dn.net/?f=%5Crm%20x%3D%5Cdfrac%7B1%7D%7B%281%2B2%29%7D%20%5B-4-%282%29%5D%2B%20%282%29%5C%5C%5C%5C%20x%20%3D%20%5Cdfrac%7B1%7D%7B3%7D%20%5Ctimes%20%28-6%29%20%2B2%20%5C%5C%0A%5C%5C%0Ax%20%3D%20-2%2B2%5C%5C%0A%5C%5C%0Ax%3D0)
![\rm y=\dfrac{m}{(m+n)} [y_2- y_1]+ y_1 \\\\ y=\dfrac{1}{(1+2)} [9-(-3)]+ (-3)\\\\ y = \dfrac{1}{3} \times (12) -3\\ \\ y = 4-3\\ \\ y =1](https://tex.z-dn.net/?f=%5Crm%20y%3D%5Cdfrac%7Bm%7D%7B%28m%2Bn%29%7D%20%5By_2-%20y_1%5D%2B%20y_1%20%5C%5C%5C%5C%20y%3D%5Cdfrac%7B1%7D%7B%281%2B2%29%7D%20%5B9-%28-3%29%5D%2B%20%28-3%29%5C%5C%5C%5C%0Ay%20%3D%20%5Cdfrac%7B1%7D%7B3%7D%20%5Ctimes%20%2812%29%20-3%5C%5C%0A%5C%5C%0Ay%20%3D%204-3%5C%5C%0A%5C%5C%0Ay%20%3D1)
Hence, the x =0 and y = 1 are coordinates of point E, which partitions the directed line segment from A to B into a ratio of 1:2.
To know more about Coordinates click the link given below.
brainly.com/question/13847533