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)?
○ g(x) = (x + 7)² + 5
○ g(x) = (x - 7)² + 5
○ g(x) = (x + 5)² + 7
○ g(x) = (x - 5)² + 7

Explanation:

Step1: Recall vertex form of parabola

The vertex form of a parabola is \(g(x) = a(x - h)^2 + k\), where \((h,k)\) is the vertex. For \(f(x)=x^2\), the vertex is \((0,0)\).

Step2: Determine translation for vertex

The vertex of \(g(x)\) is 7 units right (so \(h = 7\)) and 5 units above (so \(k = 5\)) from \(f(x)\)'s vertex. Substituting \(h = 7\) and \(k = 5\) into the vertex form, we get \(g(x)=(x - 7)^2+5\).

Answer:

B. \(g(x)=(x - 7)^2 + 5\)