Question

On a coordinate plane, an absolute value graph has a vertex at (negative 4, negative 2). Which equation represents the function graphed on the coordinate plane? g(x) = |x + 4| – 2 g(x) = |x – 4| – 2 g(x) = |x – 2| – 4 g(x) = |x – 2| + 4

Edg 2020

Answer 1

A.g(x)=|x+4|-2.

Step-by-step explanation:

Answer 2

The equation that represents the point(-4,-2) is g(x)=|x+4|-2.

Option:A.

Step-by-step explanation:

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).