Question

the graph shows g(x), which is a translation of f(x) = x². write the function rule for g(x). write your answer in the form a(x - h)² + k, where a, h, and k are integers or simplified fractions. g(x) =

Explanation:

Step1: Identify vertex

The vertex of the parabola \(g(x)\) is at \((8,0)\). In the vertex - form of a parabola \(y = a(x - h)^{2}+k\), the vertex is \((h,k)\), so \(h = 8\) and \(k = 0\).

Step2: Determine the value of \(a\)

The parent - function is \(f(x)=x^{2}\), and since there is no vertical stretch or compression (the shape of the parabola is the same as \(y = x^{2}\)), \(a = 1\).

Answer:

\(g(x)=(x - 8)^{2}+0=(x - 8)^{2}\)