Translation involves shifting of points from one position to another. The equation of the new parabola is: [tex]y = 3(x - 1)^2 - 3[/tex]
Given that:
[tex]y = 3(x + 5)^2 - 2[/tex]
[tex](h,k) = (-5,-2)[/tex] --- vertex
The general equation of a parabola is:
[tex]y = a(x - h)^2 + k[/tex]
By comparison:
[tex]a = 3\\ h = -5 \\ k= -2[/tex]
When the vertex is shifted 1 unit down, the rule is:
[tex](x,y) \to (x,y-1)[/tex]
So, we have:
[tex](x,y) \to (-5,-2-1)[/tex]
[tex](x,y) \to (-5,-3)[/tex]
When the vertex is shifted 6 unit right, the rule is:
[tex](x,y) \to (x + 6,y)[/tex]
So, we have:
[tex](h,k) \to (-5 + 6,-3)[/tex]
[tex](h,k) \to (1,-3)[/tex]
This means that:
[tex]h = 1\\ k =-3[/tex]
Recall that:
[tex]a =3[/tex]
Substitute these values in:
[tex]y = a(x - h)^2 + k[/tex]
[tex]y = 3(x - 1)^2 - 3[/tex]
Hence, the equation of the new parabola is: [tex]y = 3(x - 1)^2 - 3[/tex]
Read more about translations at:
https://brainly.com/question/12463306
