Question

f(x)=-(x - 4)^2+1 choose the correct graph of the equation.

Explanation:

Step1: Identify the vertex - form of a parabola

The general vertex - form of a parabola is $y=a(x - h)^2+k$, where $(h,k)$ is the vertex. For the function $f(x)=-(x - 4)^2+1$, we have $a=-1$, $h = 4$, and $k = 1$. So the vertex of the parabola is $(4,1)$.

Step2: Analyze the direction of the parabola

Since $a=-1<0$, the parabola opens downwards.

Step3: Check the options

We look for a parabola with vertex at $(4,1)$ and opening downwards.

Answer:

The graph with vertex at the point $(4,1)$ and opening downwards is the correct one. Without seeing the exact labels of the options, if we assume the options are labeled A, B, C, D etc., we would choose the graph that has its highest point (vertex) at the coordinates $(4,1)$ and is concave - down.