Question

fill in the equation for this function:
(image of a parabola with vertex at (5, 0) and a point at (6, 1))
f(x) = (x - 5)^2 + ?

Explanation:

Step1: Identify the vertex

The vertex form of a parabola is \( f(x) = a(x - h)^2 + k \), where \((h, k)\) is the vertex. From the graph, the vertex is at \((5, 0)\).

Step2: Substitute vertex into the equation

The given equation is \( f(x) = (x - 5)^2 + [?] \). Comparing with the vertex form, \( h = 5 \) and \( k \) is the value we need to find. Since the vertex is \((5, 0)\), \( k = 0 \). So the equation becomes \( f(x) = (x - 5)^2 + 0 \).

Answer:

\( 0 \)