Answer:
D. [tex]F(x)=(x+4)^2-5[/tex]
Step-by-step explanation:
The parent function is [tex]G(x)=x^2[/tex].
This function has its vertex at the origin (0,0).
When this function is shifted down 5 units and to the left 4 units, then its new vertex will be at (-4,-5)
The vertex form of the equation is given by;
[tex]F(x)=a(x-h)^2+k[/tex] where (h,k)=(-4,-5) is the vertex and a=1 because of the parent function.
Hence its equation is
[tex]F(x)=(x+4)^2-5[/tex]
