Question

the function $f(x)=x^2$ was transformed to create the function $g(x)=f(x - 4)-1$. what are the coordinates of the vertex of the graph of $g$? ( , ) drag these tiles and drop them in the correct blank above -1 4 -4 1 0

Explanation:

Step1: Find vertex of f(x)

The function \( f(x) = x^2 \) is a parabola with vertex at \( (0, 0) \).

Step2: Analyze transformation for g(x)

The function \( g(x) = f(x - 4) - 1 \) is a transformation of \( f(x) \). For a function \( y = f(x - h) + k \), the vertex shifts \( h \) units horizontally and \( k \) units vertically. Here, \( h = 4 \) (so shift right 4 units) and \( k = -1 \) (shift down 1 unit).

Step3: Calculate vertex of g(x)

Starting from \( (0, 0) \), shifting right 4 gives \( x = 0 + 4 = 4 \), shifting down 1 gives \( y = 0 - 1 = -1 \). So the vertex of \( g(x) \) is \( (4, -1) \).

Answer:

(4, -1)