Question 1080182
the original function is y = x^2 - 3


to reflect that function about the x-axis, the point (x,y) must become the point (x,-y)


that happens when y = f(x) becomes y = -f(x).


therefore, y = x^2 - 3 becomes y = -(x^2 - 3) which becomes y = -x^2 + 3.


to shift y = f(x) 2 units to the left, then the function becomes y = f(x+2)


therefore, y = -x^2 + 3 becomes y = -(x+2)^2 + 3.


your original function is y = x^2 - 3


your converted function that is reflected about the x-axis and shifted to the left 2 unit is y = -(x+2)^2 + 3


the first graph shows the reflection.


the second graph shows the reflection and the shift.


<img src= "http://theo.x10hosting.com/2017/050802.jpg" alt="$$$" </>


<img src= "http://theo.x10hosting.com/2017/050803.jpg" alt="$$$" </>


you can see on the first graph that -3,6 and -3,-6 are both reflections about the x-axis when x = -3, and you can see that 3,6 and 3,-6 are both reflections about the x-axis when x = 3.


you can see on the second graph that the same reflections are true, except that -3,6 on the original graph has its reflection at -5,-6 on the shifted graph, and 3,6 on the original graph has its reflection at 1,-6 on the shifted graph.


here's a reference on transformations that you might find helpful.


<a href = "https://www.mathsisfun.com/sets/function-transformations.html" target = "_blank">https://www.mathsisfun.com/sets/function-transformations.html</a>