Question

the graph shows g(x), which is a translation of $f(x) = x^2$. 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 the vertex of \( g(x) \)

The vertex form of a parabola is \( y = a(x - h)^2 + k \), where \((h, k)\) is the vertex. From the graph, the vertex of \( g(x) \) is at \((5, 0)\), so \( h = 5 \) and \( k = 0 \).

Step2: Determine the value of \( a \)

The parent function is \( f(x) = x^2 \), which has \( a = 1 \). Since \( g(x) \) is a translation (no vertical stretch or compression, just a horizontal shift), \( a = 1 \).

Step3: Write the function rule for \( g(x) \)

Substitute \( a = 1 \), \( h = 5 \), and \( k = 0 \) into the vertex form: \( g(x) = 1(x - 5)^2 + 0 \), which simplifies to \( g(x) = (x - 5)^2 \).

Answer:

\( g(x) = (x - 5)^2 \)