[important i am currently at home, i'm in summer school for algebra 1. i'm taking a pre-test, once i finish this pre-test successfully i can leave summer school. .instructions: select the correct answer from the drop-down menu. consider the absolute value function: f(x)=-|x+2|-2 the vertex of the function is: (all the answers that are listed) (2,-2) (-2,2) (-2,-2) (2,2)

The vertex of the function is:

                             (-2,-2)

We are given a absolute value function f(x) in terms of variable "x" as:

We know that for any absolute function of the general form:

the vertex of the function is : (h,k)

and if a<0 the graph of function opens downwards.

and if a>0 the graph of the function opens upwards.

Hence, here after comparing  the equation with general form of the equation we see that:

a= -1<0 , h= -2 and k= -2

Since a is negative , hence, the graph opens down .

         Hence, the vertex of the function is:

                         (-2,-2)

(-2,-2)

Step-by-step explanation:

The parent function of the absolute function is f(x)=|x|.

General form of absolute function : , where (a,b)  is the vertex of the function.

Also  , when m<0 then the graph opens downwards.

when m>0 then the graph opens upwards.

Given : The absolute value function:

Comparing the given absolute function to with the general form of the absolute function , then we get

m= -1<0 , a= -2 and b= -2

Since m is negative , it means the graph of the function opens downwards .

∴, the vertex of the function is : (-2,-2)

the system of inequity is

step-by-step explanation:

from the given graph it is noticed that we have two related lines. one is solid and another is dashed.

if a line passing through two points, then the equation of line is

the solid line passing through the points (0,4) and (4,0).

the related equation of solid line is .

similarly, find the related equation of dashed line. the dashed liune passing through the points (0,0) and (3,1).

the related equation of dashed line is

from the given graph it is noticed that the point (0,1) lies on the shaded region, therefore the point (0,1) must be satisfied by the related equations.

check the related equations by the point (0,1).

this statement is true if the sign of inequality is < instead of equality. since it is an solid line therefore the sign of inequality will be . the required inequality is

similarly, check the second related equation.

it is a dashed line, so this statement is true if the sign of inequality is > . the required inequality is