Use the equation \( y=x^{2}-9 \) to answer parts a) through g) below. a) Determine whether the parabola will open upward or downward. T. The parabola will open downward. b) Find the equation of the axis of symmetry. The axis of symmetry is \( x=0 \). (Type an equation.) c) Find the vertex. The vertex of the parabola is (Type an ordered pair.)

Let's analyze the given equation of the parabola, \( y = x^2 - 9 \), step by step. ### a) Determine whether the parabola will open upward or downward. The general form of a parabola is \( y = ax^2 + bx + c \). In this case, we have: - \( a = 1 \) - \( b = 0 \) - \( c = -9 \) Since \( a > 0 \), the parabola opens **upward**. ### b) Find the equation of the axis of symmetry. The axis of symmetry for a parabola in the form \( y = ax^2 + bx + c \) is given by the formula: \[ x = -\frac{b}{2a} \] Substituting the values of \( a \) and \( b \): \[ x = -\frac{0}{2 \cdot 1} = 0 \] Thus, the equation of the axis of symmetry is: \[ x = 0 \] ### c) Find the vertex. The vertex of a parabola can be found using the coordinates: \[ \left(-\frac{b}{2a}, f\left(-\frac{b}{2a}\right)\right) \] We already calculated \( -\frac{b}{2a} = 0 \). Now we need to find \( f(0) \): \[ f(0) = 0^2 - 9 = -9 \] Thus, the vertex of the parabola is: \[ (0, -9) \] ### Summary of Answers: - a) The parabola will open **upward**. - b) The axis of symmetry is \( x = 0 \). - c) The vertex of the parabola is \( (0, -9) \).