Answer:
f(x) = -(x-3)(x-3) + 4
Explanation:
To change f(x) = -(x-3)^2+4 to factored form, we can use the vertex form of the equation of a parabola, which is f(x) = a(x-h)^2 + k, where (h,k) is the vertex of the parabola and a is a constant that determines the shape of the parabola.
First, we need to factor out the negative sign in the equation, which gives us:
f(x) = -1(x-3)^2 + 4
Now, we can see that the vertex of the parabola is (3, 4), which means that h=3 and k=4. We also know that the negative value of the coefficient means that the parabola is facing downwards.
Using this information, we can write the factored form of the equation as:
f(x) = -1(x-3)^2 + 4
f(x) = -1(x-3)(x-3) + 4
f(x) = -(x-3)(x-3) + 4
So the factored form of f(x) = -(x-3)^2+4 is f(x) = -(x-3)(x-3) + 4.