Question

Select the graph of y = – |x + 2| + 3

Answer 1

what are the options?

Answer 2

Since the absolute value of a number is always positive,
When we graph the equation y = – |x + 2| + 3 the shape of our graph looks quite different from the graph of y = – (x + 2) + 3.
(see the attached graph below for more detail)
The graph of every linear absolute value always has an inverted "V" or a sideways "V" shape. This "V" is the result of the negative absolute values becoming positive.
The global maximum point is when -|x+2| is 0, that is when x=-2 (A).
When y = – |x + 2| + 3 = 0, we can find the two points intersecting the x-axis (B, C).