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

On a coordinate plane, an absolute value graph has a vertex at (negative 2, 4).

On a coordinate plane, an absolute value graph has a vertex at (4, 2).

On a coordinate plane, an absolute value graph has a vertex at (2, 4).

The following graph represents the function g(x)=|x+4| +2

1) On a coordinate plane, an absolute value graph has a vertex at (-4,2)

Step-by-step explanation:

A vertex can bed defined as a point where two lines meet. In a graph, a vertex can also be interpreted as the point where the direction of the line or curve change

The function is given by:

which is an absolute value function. We need to find the vertex of the graph.

The graph drawn is attached below.

We can see in the graph that at x = -4 and y = 2 , a point is formed where the straight line changes its direction.

So the vertex is formed at (-4,2)

The equation that represents this situation is x + 3x + (x - 4) + 2(x - 4) = 72, where x is Erik's age

Step-by-step explanation:

Let us solve the question

Assume that Erik is x years old

∵ Erik is x years old

∵ Erik is as old as Dawn

→ That means x = Dawn

∴ x = Dawn

→ Multiply both sides by 3

∴ 3x = Dawn

∴ Dawn is 3x years old

∵ Jiro is 4 years younger than Erik

→ That means Jiro = x - 4

∴ Jiro is (x - 4) years old

∵ Alita is 2 times as old as Jiro

→ That means Alita = 2 × (x - 4)

∴ Alita = 2 × (x - 4)

∴ Alita is 2(x - 4) years old

∵ The sum of all their ages is 72

→ That means add their ages and equate the sum by 72

∴ Erike's age + Dawn's age + Jiro's age + Alita's age = 72

∴ x + 3x + (x - 4) + 2(x - 4) = 72

The equation that represents this situation is x + 3x + (x - 4) + 2(x - 4) = 72, where x is Erik's age