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: Identify vertex of $f(x)$

The vertex of $f(x)=x^2$ is $(0,0)$.

Step2: Find vertex of $g(x)$

Shift right 7, up 5: $(0+7, 0+5)=(7,5)$.

Step3: Use vertex form of parabola

Vertex form: $g(x)=(x-h)^2+k$, where $(h,k)$ is vertex. Substitute $(h,k)=(7,5)$:
$g(x)=(x-7)^2+5$

Answer:

$g(x)=(x-7)^2+5$