Question

Given the function f(x) = -|x + 3| + 2, answer the following questions:

Vertex:
a) (-3, 2)
b) (3, -2)
c) (0, 2)
d) (2, 0)

Answer 1

The vertex of the function f(x) = -|x + 3| + 2 is at the point where the inside of the absolute value is zero. Solving x + 3 = 0 gives us x = -3, and substituting it back into the function gives us f(-3) = 2. Thus, the vertex is (-3, 2).

Step-by-step explanation:

To find the vertex of the function f(x) = -|x + 3| + 2, you need to understand how the absolute value function behaves. The vertex of an absolute value function is at the point where the expression inside the absolute value is zero because it is the highest or lowest point of the graph, depending on whether the function opens up or down. In this case, setting the expression inside the absolute value to zero gives us x + 3 = 0, which simplifies to x = -3. Substituting x back into the function gives us f(-3) = -|(-3) + 3| + 2, ultimately resulting in f(-3) = 2. Therefore, the vertex of the function is at the point (-3, 2).