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.
-$$y = 5 x ^ { 2 } + 5$$
A) $y$-axis only
B) $x$-axis, $y$-axis, origin
C) $x$-axis only
D) origin only

Question

Quizplus · Accepted Answer

The equation $y = 5x^2 + 5$ is a parabola opening upwards with its vertex at the origin. This makes it symmetric about the $y$-axis because for every point $(x, y)$ on the graph, the point $(-x, y)$ is also on the graph. This symmetry does not extend to the $x$-axis or the origin.

Determine Whether the Equation Has a Graph That Is Symmetric y=5x2+5y = 5 x ^ { 2 } + 5y=5x2+5

Determine Whether the Equation Has a Graph That Is Symmetric $y = 5 x ^ { 2 } + 5$