Based on the image, the graph is a parabola with a vertex at (4, 3) and another point at (5, 1). The quadratic function can be written in vertex form:

$g(x) = a(x - h)^2 + k$

where $(h, k)$ is the vertex. Here, $h = 4$ and $k = 3$, so:

$g(x) = a(x - 4)^2 + 3$

To find $a$, use the point $(5, 1)$ that lies on the curve:

$1 = a(5 - 4)^2 + 3$

Simplifying:

$1 = a(1)^2 + 3$ $1 = a + 3$ $a = -2$

Thus, the equation of the quadratic function is:

$g(x) = -2(x - 4)^2 + 3$