Match the Quadratic Function y=-(x-4)² to Its Graph: Visual Analysis

One function

$y=-(x-4)^2$

for the corresponding chart

The problem involves matching a given function $y = -(x-4)^2$ with its corresponding graph from multiple choices.

First, let's analyze the function:

• The function is in vertex form $y = a(x-h)^2 + k$, where the vertex is $(h, k)$.
• Here, $a = -1$, $h = 4$, and $k = 0$, so the vertex is $(4, 0)$.
• The negative sign indicates the parabola opens downward.

To match the function with the correct graph:

• Identify that the vertex of the parabola is at $(4, 0)$.
• The parabola is symmetric around the line $x = 4$, opening downwards.

Upon examining the choices, Option 1 clearly shows a parabola with a vertex at $(4, 0)$ opening downward. This matches perfectly with the function $y = -(x-4)^2$.

Therefore, the correct answer to the problem is 1.