Symmetry — Quiz

Question 5 • Algebra II

Which graph shows rotational symmetry?

Answer

Image with description On a coordinate plane, the x and y axes range from negative 5 to 5 in increments of 1. The graph has a curve g of x split into two small curves so that one curve is the mirror image of the other. The first curve goes through the points (negative 3 comma negative 2) and (0 comma 0). The second curve goes through (0 comma 0) and (2 comma 3).

Image with description On a coordinate plane, the x and y axes range from negative 5 to 5 in increments of 1. The graph is a v-shaped curve h of x that opens downwards with vertex at (0 comma 0). The curve goes through (negative 4 comma negative 4) and (4 comma negative 4).

Image with description On a coordinate plane, the x and y axes range from negative 5 to 5 in increments of 1. The graph has a parabola k of x opens upwards with vertex at (0 comma 0). It goes through (negative 2 comma 4) and (2 comma 4).

Image with description On a coordinate plane, the x and y axes range from negative 5 to 5 in increments of 1. The graph has a curve f of x with crests and troughs and passes through the origin. The crest is at (negative 2 comma 2), and the trough is at (2 comma negative 2). The curve has 3 x-intercepts.

Explanation

A graph has rotational symmetry about the origin if rotating it 180° maps it onto itself; corresponding points have opposite coordinates. In B, the crest at (−2, 2) corresponds to the trough at (2, −2), and the curve passes through the origin. This shows the curve has symmetry under a half-turn, so B is the graph with rotational symmetry.

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