draw a complete graph so that it has y - axis symmetry. choose the correct graph below.

Explanation:

Step1: Recall the property of y - axis symmetry

A graph has y - axis symmetry if for every point ((x,y)) on the graph, the point ((-x,y)) is also on the graph.

Step2: Analyze the given points

We have points ((0, - 4)), ((1,-3)), ((2,0)). For y - axis symmetry:

• When (x = 0), (-x=0), and the point ((0, - 4)) is on the y - axis.
• When (x = 1), (-x=-1). So there should be a point ((-1,-3)) on the graph.
• When (x = 2), (-x = - 2). So there should be a point ((-2,0)) on the graph.

Step3: Check each option

• Option A: Does not have the symmetric points ((-1,-3)) and ((-2,0))
• Option B: Does not have the symmetric points ((-1,-3)) and ((-2,0))
• Option C: Does not have the symmetric points ((-1,-3)) and ((-2,0))
• Option D: Has the points ((0, - 4)), ((1,-3)), ((2,0)) and their symmetric counterparts ((-1,-3)), ((-2,0))

Answer:

D.