Find the coordinates of the vertex for the parabola defined by the given quadratic function. $$ f(x)=-x^{2}+4 x+5 $$ The vertex is $$ \square $$. (Type an ordered pair.)

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To find the vertex of the parabola defined by the quadratic function $$ f(x) = -x^2 + 4x + 5 $$, we can use the vertex formula for a quadratic function in the form $$ f(x) = ax^2 + bx + c $$. The x-coordinate of the vertex is given by:

$$
x = -\frac{b}{2a}
$$

In this case, $$ a = -1 $$ and $$ b = 4 $$. Plugging in these values:

$$
x = -\frac{4}{2(-1)} = -\frac{4}{-2} = 2
$$

Now, we need to find the y-coordinate of the vertex by substituting $$ x = 2 $$ back into the function $$ f(x) $$:

$$
f(2) = - (2)^2 + 4(2) + 5
$$
$$
= -4 + 8 + 5
$$
$$
= 4 + 5 = 9
$$

Thus, the coordinates of the vertex are $$ (2, 9) $$.

The vertex is $$ \boxed{(2, 9)} $$.
The vertex is $$ (2, 9) $$.

Find the coordinates of the vertex for the parabola defined by the given quadratic function. \( f(x)=-x^{2}+4 x+5 \) The vertex is \( \square \). (Type an ordered pair.)

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