For a quadratic with a vertex of (4, 1) with the graph opening downward, is this the right construction in vertex form?

-a(x - 4) + 1

It's good. You don't really need the leading "-" if you say a is negative, but having it there does signal your intentions clearly.

Actually, the assignment says the graphs opens downward and asks me to put in in the equation. So then this looks fine, right?

To determine whether the given quadratic expression represents the correct equation in vertex form, let's go through the steps to find the vertex form of a quadratic equation.

The vertex form of a quadratic equation is given by:

y = a(x - h)^2 + k

Where (h, k) represents the vertex of the parabola, and a determines the direction and stretch of the graph.

Given that the vertex is (4, 1) and the graph opens downwards, let's plug these values into the vertex form:

y = a(x - 4)^2 + 1

Now, we need to determine the appropriate value of "a.". Since the graph opens downward, a must be a negative value.

If we further simplify the equation, we have:

y = a(x^2 - 8x + 16) + 1
y = ax^2 - 8ax + (16a + 1)

Comparing this form with the given expression -a(x - 4) + 1, we can see that the coefficients of the quadratic term (x^2), the linear term (x), and the constant term (1) don't match.

Therefore, the given expression -a(x - 4) + 1 does not represent the correct equation in vertex form for a quadratic with a vertex of (4, 1) opening downward.

To find the correct expression, we must solve for "a" using additional information, such as points on the graph or the equation of the axis of symmetry.