state the transformations: f(x)= -3(x-3)^2+4

We are asked to state the transformations in the following
quadratic equation: f(x) = -3(x-3)^2 + 4.

This is an
equation for a parabola.

The parent graph of this equation
is f(x) = x^ 2, where the vertex of a parabola is at (0,0) and the parabola opens
upward.

The equation in this problem is in the form of f(x)
= a(x-h)^2 + k.

The transformed vertex is given by (h,k) in
the equation.

The vertex of the parabola in
the given problem is at
(3,4).

The parabola opens
downward because the "a" value in the transformed equation is negative.

Since the a value is a whole
number the parabola will "shrink," meaning that its graph will be narrower than the
parent graph.