Answer:
Reflection across the x-axis: y = − f ( x ) y = -f(x) y=−f(x) The concept behind the reflections about the x-axis is basically the same as the reflections about the y-axis. The only difference is that, rather than the y-axis, the points are reflected from above the x-axis to below the x-axis, and vice versa.
the equation for g(x) after reflected over x axis and translated 4 units left
[tex]g(x)=-(x+4)^2[/tex]
Given :
Parent function is [tex]f(x)=x^2[/tex]
When a graph is reflected over x-axis then f(x)=-f(x)
When a graph is translated 'a' units left then we add 'a' with
f(x) becomes f(x+a)
Parent function f(x) is reflected over x-axis , multiply -1 with f(x)
so , [tex]f(x)=-x^2[/tex]
Now we translate 4 units to the left, add 4 with x
[tex]g(x)=-x^2\\g(x)=-(x+4)^2[/tex]
The final equation of g(x) is
[tex]g(x)=-(x+4)^2[/tex]
Learn more : brainly.com/question/9111027
