what is the equation of the translated function?\n○ (f(x)=(x - 1)^2-5)\n○ (f(x)=(x + 1)^2+5)\n○ (f(x)=(x…

Explanation:

Step1: Recall vertex - form of quadratic function

The vertex - form of a quadratic function is $y = a(x - h)^2+k$, where $(h,k)$ is the vertex of the parabola. The original function is $f(x)=x^2$ with vertex $(0,0)$.

Step2: Identify the vertex of the translated function

From the graph, the vertex of the translated parabola is at $(1, - 5)$.

Step3: Substitute the vertex values into the vertex - form

Substituting $h = 1$ and $k=-5$ into $y=a(x - h)^2 + k$ (since $a = 1$ as the shape of the parabola is the same as $y=x^2$), we get $y=(x - 1)^2-5$.

Answer:

$f(x)=(x - 1)^2-5$