Graph the given quadratic function. Identify the vertex, axis of symmetry, intercepts, domain, range, and intervals for which the function is increasing or decreasing. $f\left(x\right)=-\left(x-5\right)^2+1$

• A.
• B.
• C.
• D.

Answer: (A)

Verified step by step guidance

1. Identify the standard form of the quadratic function: f(x) = a(x-h)^2 + k, where (h, k) is the vertex.
2. For the given function f(x) = -(x-5)^2 + 1, identify the vertex (h, k) as (5, 1).
3. Determine the axis of symmetry, which is the vertical line x = h. Here, it is x = 5.
4. Find the y-intercept by setting x = 0 in the function: f(0) = -(0-5)^2 + 1.
5. Determine the intervals of increase and decrease. Since the parabola opens downwards (a < 0), it decreases on (-∞, 5) and increases on (5, ∞).