How do you graph #f(x) =-2abs(4x-1)+16#?

To graph the function ( f(x) = -2 \cdot |4x - 1| + 16 ), follow these steps:

1. Identify the vertex of the absolute value function ( |4x - 1| ), which occurs when the expression inside the absolute value is equal to zero. So, solve ( 4x - 1 = 0 ) to find the x-coordinate of the vertex.
2. Once you find the x-coordinate of the vertex, substitute it back into the original function to find the corresponding y-coordinate.
3. Plot the vertex on the coordinate plane.
4. Determine the direction of the absolute value function. Since the coefficient of ( |4x - 1| ) is negative (-2), the graph will open downwards.
5. Choose a few points to the left and right of the vertex and plug them into the function to find their corresponding y-values.
6. Plot these points on the graph.
7. Connect the points smoothly to form the graph of the function.