Use the equation \( f(x)=x^{2}+4 x-7 \), to answer parts a) through g). a) Determine whether the parabola opens upward or downward. The parabola opens downward. The parabola opens upward. The axis of symmetry is \( x=-2 \) of 8 . (Type an equation.) c) Find the vertex. The vertex of the parabola \( f(x)=x^{2}+4 x-7 \) is 1 ( \( \left.12,-11\right) \). (Type an ordered pair.) d) Find the \( y \)-intercept. The \( y \)-intercept of \( f(x)=x^{2}+4 x-7 \) is (Type an ordered pair.)

The equation you provided \( f(x) = x^2 + 4x - 7 \) is a quadratic function, where the coefficient of \( x^2 \) is positive, meaning the parabola opens upward. This can be quickly determined since a positive leading coefficient indicates an upward opening. Next, to find the vertex of the parabola, you can use the vertex formula \( x = -\frac{b}{2a} \). Here, \( a = 1 \) and \( b = 4 \), so \( x = -\frac{4}{2(1)} = -2 \). Plugging this back into the function gives you the \( y \)-coordinate, resulting in the vertex at the point \( (-2, -11) \). For the \( y \)-intercept, which occurs where \( x = 0 \), substitute \( 0 \) into the function: \( f(0) = 0^2 + 4(0) - 7 = -7 \). Therefore, the \( y \)-intercept is at the point \( (0, -7) \).