For the quadratic function \( f(x)=x^{2}+6 x+9 \), answer parts (a) through (f). (a) Find the vertex and the axis of symmetry of the quadratic function, and determine whether the graph is concave up or concave down. The vertex is \( \square \). (Type an ordered pair, using integers or fractions.)

The vertex of the quadratic function \( f(x) = x^2 + 6x + 9 \) can be found by rewriting it in vertex form or using the formula for the vertex, which is \( \left(-\frac{b}{2a}, f\left(-\frac{b}{2a}\right)\right) \). Here, \( a = 1 \) and \( b = 6 \). Thus, the x-coordinate of the vertex is \( -\frac{6}{2 \cdot 1} = -3 \). Plugging \( -3 \) back into the function gives \( f(-3) = (-3)^2 + 6(-3) + 9 = 0 \). So, the vertex is \( (-3, 0) \). The axis of symmetry is a vertical line through the vertex, which is \( x = -3 \). Since the coefficient of \( x^2 \) is positive, the graph is concave up. The vertex is \( (-3, 0) \).