the graph shows g(x), which is a translation of f(x) = x². write the function rule for g(x). write your…

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) =

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) =

Answer

Explanation:

Step1: Identify vertex form of quadratic

The vertex - form of a quadratic function is $y = a(x - h)^2+k$, where $(h,k)$ is the vertex of the parabola.

Step2: Locate the vertex

From the graph, the vertex of the parabola $g(x)$ is at $(7,- 4)$. So, $h = 7$ and $k=-4$.

Step3: Determine the value of a

Since the parabola $g(x)$ is a translation of $f(x)=x^{2}$ and has the same shape (no vertical stretch or compression other than a possible sign - change), $a = 1$.

Answer:

$g(x)=(x - 7)^2-4$