Question

The graph of g(x) is a translation of the function f(x)=x². The vertex of g(x) is located 5 units above and 7 units to the right of the vertex of f(x). Which equation represents g(x) ?

A) g(x)=(x+7)²+5
B) g(x)=(x-7)²+5
C) g(x)=(x+5)²+7
D) g(x)=(x-5)²+7

Answer 1

An equation representing a translation of the vertex of a quadratic function by 5 units up and 7 units to the right is g(x) = (x - 7)² + 5.

Step-by-step explanation:

The student's question is looking for the equation of a function g(x) which is a translation of the function f(x) = x². Specifically, g(x)'s vertex is 5 units above and 7 units to the right of the vertex of f(x). In function notation, a translation to the right is represented by subtracting from the x variable, and moving the graph up is represented by adding to the entire function. Thus, the correct equation that represents g(x) with these translations would be g(x) = (x - 7)² + 5.