Question

The graph shows g(x), which is a translation of f(x)=x2. Write the function rule for g(x)

Answer 1

g(x) = x^2 -3

Explanation:

First of all we see that the graph is shifted downward (f(0)=0^2=0)

let g(x) = f(x) + c = x^2 + c

where c is a constant

from the graph we know that:

g(0) = -3

0^2 + c = -3

c = -3

so g(x) = x^2 -3

then plug in some points to see if its true:

g(2) = 2^2 - 3 = 1 ### correct

g(3) = 3^2 - 3 = 6 ### correct