What is the vertex of the graph of f(x) = |x + 7| - 4?

Answer 1

The important thing to remember here is that the vertex of f(x) = |x| is located at the origin, (0,0).

In the form f(x) = a|x-h| + k, the h-value translates the graph left/right and the k-value translates the graph up/down. The vertex will move as far as the h- and k-values indicate.

In the function, f(x) = |x + 7| - 4, the h-value is -7, and the k-value is -4.

So the vertex of the function moves from the origin, (0,0) and translates 7 units left and 4 units down. Thus, the vertex is located at (-7,-4).

Hope this helps!

Answer 2

Hi Ryan,

We can use vertical and horizontal translations to find the vertex.

When a function is in the form f(x) = |x+a|-b , the vertex is equal to (-a,b).

In the function f(x) = |x+7|-4, a= 7 and b= - 4

Therefore the vertex = (-a,b) = (-7,-4) .