Q. 80 - Precalculus Enhanced with Graphing Utilities

Question

If the graph of an equation is symmetric with respect to the $x$-axis and $2$ is a $y$-intercept, name another $y$-intercept.

Step-by-Step Solution

Answer

The other $y$-intercept is $-2$.

Step 1: Given information

The graph of the given equation is symmetric to the $x$-axis and $y$-intercept is 2 .

Step 2: Determine the other y -intercept.

As the $y$-intercept is $2$ therefore the point $(0,2)$ is on the axis.

When the graph of an equation is symmetric with respect to the $x$-axis, then if point $(x, y)$ is on the graph, so is the point $(x,-y)$.

Therefore, the point $(0,-2)$ is also on the graph of the equation.

Step 3: Write the conclusion

The $y$-intercept is $-2$.