Determine whether the equation has a graph that is symmetric with respect to the y -axis, the x-axis, the origin, or none
of these.
-y = (x - 6)(x + 3)
A) y-axis only
B) none of these
C) x-axis only
D) x-axis, y-axis, origin

Question

Quizplus · Accepted Answer

The equation y = (x - 6)(x + 3) is a quadratic equation, which means its graph is a parabola. This particular parabola does not exhibit symmetry with respect to the y-axis, x-axis, or the origin. The symmetry of a graph relative to the y-axis implies that for every point (x, y) on the graph, the point (-x, y) is also on the graph, which is not the case here due to the non-symmetric placement of its roots (-3 and 6) with respect to the y-axis. It does not exhibit symmetry with respect to the x-axis because it is not a function that produces the same y-value for both a positive and negative x-value. Lastly, it does not exhibit origin symmetry because for every point (x, y) on the graph, the point (-x, -y) is not also on the graph, as required for origin symmetry.

Determine Whether the Equation Has a Graph That Is Symmetric