What is the y-value of the vertex of the function f(x) = –(x – 3)(x + 11)?

the y-value of the vertex is

.

49

Step-by-step explanation:

Given

f(x) = - (x - 3)(x + 11)

Find the zeros by setting f(x) = 0, that is

- (x - 3)(x + 11) = 0

Equate each factor to zero and solve for x

x - 3 = 0 ⇒ x = 3

x + 11 = 0 ⇒ x = - 11

The vertex lies on the axis of symmetry which is situated at the midpoint of the zeros

= = = - 4

Substitute x = - 4 into f(x) for y- coordinate of vertex

f(- 4) = -(- 7)(7) = 49 ← y- value of vertex

so firstly, we need to isolate the y variables to be able to solve these inequalities. firstly, add 0.5x on both sides of the first inequality and subtract 1.5x on both sides of the second inequality:

now since the slope is positive for the first inequality, this means that the line going upwards belongs to the first inequality, and the line going downwards belongs to the second inequality.

next, since y ≥ in the first inequality, this means that the shaded region will be above the first inequality's line, thus shading regions a and b.

next, since y ≤ in the second inequality, this means that the shaded region is going to be below this line, thus shading regions a and c.

since both lines shade region a, this means that region a is the solution.

step-by-step explanation:

mark brainliest!