Answer:
(-3, -2)
Explanation:
The vertex of a graph of a quadratic function is the point where the graph reaches its minimum or maximum value, and it can be found by completing the square.
To find the vertex of the graph F(x) = |x+3| -2, we can rewrite the function as follows:
F(x) = (x+3) - 2, if x+3 ≥ 0
F(x) = -(x+3) - 2, if x+3 < 0
The first equation represents the portion of the graph where x+3 is positive, and the second equation represents the portion of the graph where x+3 is negative.
To find the vertex of the graph, we can find the average of the zeros of the function. The zeros of the function are the values of x that make the function equal to 0.
The zeros of the first equation are found by setting the expression equal to 0 and solving for x:
x+3-2 = 0
x = -1
The zeros of the second equation are found by setting the expression equal to 0 and solving for x:
-(x+3)-2 = 0
-(x+3) = 2
x = -5
The average of the zeros is (-1 + -5) / 2 = -3. This is the x-coordinate of the vertex of the graph.
To find the y-coordinate of the vertex, we can plug the x-coordinate into one of the equations and solve for y:
F(-3) = (-3+3) - 2 = -2
Therefore, the vertex of the graph F(x) = |x+3| -2 is (-3, -2).