Answer:
D
Step-by-step explanation:
Let us start with the standard equation of a parabola, [tex]y=a(x-h)^2+k[/tex]. To move the parabola up or down, we would change the value of k. k>0, the parabola goes upward. k<0, the parabola goes downward. To move the parabola left or right, we would change the h value. h>0, the parabola goes to the right. h<0, the parabola goes to the left. Also take note that a change of 1 unit on an h or k value reflects also a 1 unit translation on the graph of the parabola.
The question asks us to shift our parabola [tex]g(x)=4x^2-16[/tex] right 7 units and down 3 units. Therefore, we have:
[tex]g(x)=4(x-7)^2-16-3\\g(x)=4(x-7)^2-19[/tex]
D
I hope this helps! Let me know if you have any questions :)
