Choose the function that represents the graph of the transformation of f (x) = |x| that opens down and has a vertex of (3,2)

f (x) = |x - 3| - 2

f (x) = - |x - 3| + 2

f (x) = |x + 3| + 2

f (x) = - |x + 3| + 2

f (x) = - |x - 3| + 2.

Step-by-step explanation:

f (x) = |x| is shaped like a V and the vertex is at (0, 0). f (x) = - |x| is a reflection in the x-axis so will be an inverted V, opening down. f (x) = - |x - 3| will be the - |x| moved 3 units to the right with the vertex at (3, 0). To bring the vertex to (3, 2) it will move upwards 2 units.

So it is f (x) = - |x - 3| + 2.

f (x) = -|x-3|+2

Negative before the abs value inverts the graph and it moves right 3 and up 2