Determine whether the graph of the equation is symmetric with respect to the x-axis, the y-axis, and/or the origin.
-$$y = ( x + 3 ) ( x + 7 )$$
A) $y$-axis
B) origin
C) $x$-axis
D) $x$-axis, $y$-axis, origin
E) none

Question

Quizplus · Accepted Answer

The equation $y = (x + 3)(x + 7)$ is a quadratic equation in standard form, which represents a parabola. To check for symmetry:  - For x-axis symmetry, replace $y$ with $-y$ and see if the equation remains unchanged. It does not, so no x-axis symmetry.  - For y-axis symmetry, replace $x$ with $-x$ and see if the equation remains unchanged. It does not, so no y-axis symmetry.  - For origin symmetry, replace $x$ with $-x$ and $y$ with $-y$ and see if the equation remains unchanged. It does not, so no origin symmetry.  Thus, the graph is not symmetric with respect to any of the axes or the origin.

Determine Whether the Graph of the Equation Is Symmetric with Respect