Answer:
[tex]g(x)=-(x+1)^2-4[/tex].
Step-by-step explanation:
The parent function is
[tex]f(x)=x^2[/tex]
Step 1: Start with the equation [tex]f(x)=x^2[/tex]. Write the equation for the graph of g(x) that has been
reflected, or flipped, over the x-axis.
[tex]f_1(x)=-f(x)[/tex]
[tex]f_1(x)=-x^2[/tex]
Use the equation you wrote in Step 1. Write the equation for the graph of g(x) that has
also been shifted down 4 units.
[tex]f_2(x)=f_1(x)-4[/tex]
[tex]f_2(x)=-x^2-4[/tex]
Step 3: Use the equation you wrote in Step 2. Write the equation for the graph of g(x) that has
also been shifted left 1 unit.
[tex]g(x)=f_2(x+1)[/tex]
[tex]g(x)=-(x+1)^2-4[/tex]
Therefore, the required equation is [tex]g(x)=-(x+1)^2-4[/tex].
