Question

Write a function g with the parent function f(x)=x^2 that has a vertex at (3,-6)

Answer 1

`g(x)=(x-3)^2-6`

Explanation:

we have

The parent function is

`f(x)=x^(2)` -----> The vertex is the point (0,0)

The function g(x) has a vertex at (3,-6)

so

The rule of the translation of f(x) to g(x) is

(x,y) ------> (x+3, y-6)

That means ----> The translation is 3 units at right and 6 units down

therefore

The equation of the function g(x) is

`g(x)=(x-3)^2-6`