Answer:
The equation that represents the point(-4,-2) is g(x)=|x+4|-2.
Option:A.
<u>Explanation:</u>
The given vertices are (-4,-2).
Substitute the vertices in the equations and equate the values to find the equation.
The value given inside the modulus is always positive. eg: |-4|=|4|.
Substitute the vertices in equation g(x)=|x+4|-2.
-2=|-4+4|-2.
-2=0-2.
-2=-2.
∴ The equation g(x)=|x+4|-2 has the vertex (-4,-2).
Check with other equation to confirm the answer.
Substitute the vertices in equation g(x)=|x-4|-2.
-2=|-4-4|-2.
-2=8-2.
-2≠6.
∴ The equation g(x)=|x-4|-2 doesn't has the vertex (-4,-2).
Substitute the vertices in equation g(x)=|x-2|-4.
-2=|-4-2|-4.
-2=6-4.
-2≠2.
∴ The equation g(x)=|x-2|-4 doesn't has the vertex (-4,-2).
Substitute the vertices in equation g(x)=|x-2|+4.
-2=|-4-2|+4.
-2=6+4.
-2≠10.
∴ The equation g(x)=|x-2|+4 doesn't has the vertex (-4,-2).
