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.
-$$y = 3 x ^ { 2 } + 4$$
A) $x$-axis, $y$-axis, origin
B) $x$-axis only
C) $y$-axis only
D) origin only

Question

Quizplus · Accepted Answer

The equation $y = 3x^2 + 4$ is a parabola that opens upwards. It is symmetric with respect to the y-axis because replacing $x$ with $-x$ yields the same equation, indicating that for every point $(x, y)$ on the graph, there is a corresponding point $(-x, y)$ also on the graph. It is not symmetric with respect to the x-axis or the origin.

Determine Whether the Equation Has a Graph That Is Symmetric y=3x2+4y = 3 x ^ { 2 } + 4y=3x2+4

Determine Whether the Equation Has a Graph That Is Symmetric $y = 3 x ^ { 2 } + 4$