Match the Quadratic Function y=-(x-5)² to Its Correct Graph

One function

$y=-(x-5)^2$

for the corresponding chart

We need to match the function $y = -(x-5)^2$ to the correct graph.

• The graph will be a parabola that opens downward because of the negative sign in front.
• The vertex of this parabola is $(5, 0)$ due to the function $y = -(x-5)^2$.

Let’s analyze the characteristics of the graph:

• The parabola is concave down (opens downward) since the square term is negative.
• The vertex point of our equation must be located at $(5, 0)$.
• This point indicates that the graph's highest point is at $x = 5$.

Reviewing the options given in the chart, Option 1 correctly shows the vertex of the parabola at point $(5, 0)$, and it opens downward, as expected from a negative quadratic function.

The graph in accordance with the given function is option 1.