write the function whose graph is the graph of` y=(x+3)^2` but is reflected about the x axis.

Expert Answers
lemjay eNotes educator| Certified Educator

Note that when a function y=f(x) is reflected about the x-axis, the new equation is y=-f(x). This means that when reflected about the x-axis, all original values of y are multiplied by -1. So we have,


Then, multiply right side by -1.


So, it's reflection about the x-axis is `y=-(x+3)^2` .

Let's refer to the graph of `y=(x+3)^2` and it's reflection about the x-axis to verify.

The graph of  `y=(x+3)^2 ` is the red curve. And the graph of `y=-(x+2)^2` is the blue curve. Both curves have the same x-coordinates. But the y-coordinates of the blue graph is the negative values of y of the other. So this proves that the blue curve is the reflection of the red curve about the x-axis.

Hence, the reflection of `y=(x+3)^2` about the x-axis is `y=-(x+3)^2` .