Question

If the graph of an equation is symmetric with respect to the $y$-axis and 6 is an $x$-intercept of this graph, name another $x$-intercept.

Short answer

The other $x$-intercept is $-6$.

Step-by-step solution

Given information

The $x$-Intercept is $6$, therefore the graph intersects the $x$-axis at $(6,0)$.

Determine the other point.

Since the graph is symmetric with respect to the $y$-axis, the following point is also on the graph:

$(-(6),0)$

Simplify the expression for the first coordinate by changing the sign of the number:

$(-6,0)$

Therefore, the graph contains the point $(-6,0)$.

The graph intersects the $x$-axis at $(6,0)$because the $y$-coordinate is 0 .

Since the graph intersects the $x$-axis at $(-6,0)$, the $x$-intercept occurs at$-6$.

Write the conclusion

The other $x$-interceptis $-6$.