Question

A new parabola, g(x), is translated from f(x) using the translation T(-3, 7).

5. What is the vertex point of g(x)?
Explain how you know.

Answer 1

We can predict the vertex point of
`g(x)` by vectorial sum, which is equal to
`V_(G)(x,y) = (h - 3, k + 7)`.

Explanation:

The vertex of
`g(x)` is equal to the vectorial sum of the vertex of
`f(x)` and the translation vector:

`V_(G)(x,y) = V_(F)(x,y) + T(x,y)` (1)

Where
`T(x,y)` is the translation vector.

If we know that
`V_(F) (x,y) = (h,k)` and
`T(x,y) = (-3, 7)`, then the formula for the vertex of
`g(x)` is:

`V_(G)(x,y) = (h,k) +(-3, 7)`

`V_(G)(x,y) = (h - 3, k + 7)`