Question

Find the vertex of the graph.
F(x) = |x+3| -2

Answer 1

The vertex of the graph is at the point (-3, -2).

Explanation:

The graph of the function F(x) = |x+3| - 2 will have a vertex at the point where the graph changes direction.

This occurs when the derivative of the function is equal to zero.

To find the derivative of the function F(x) = |x+3| - 2, we can use the following steps:

1. Break the function down into two separate cases, one for x < -3 and one for x ≥ -3.
2. For x < -3, the function is equal to -(x+3) - 2, so the derivative is -1.
3. For x ≥ -3, the function is equal to (x+3) - 2, so the derivative is 1.

Since the derivative is equal to zero at x = -3, the vertex of the graph is at the point (-3, -2).