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. \( x \) The parabola opens dowrward. b) Find the parabola opens upward. The axis of symmetry is \( x=-2 \). (Type an equation.) c) Find the vertex. The vertex of the parabola \( f(x)=x^{2}+4 x-7 \) is (Type an ordered pair.)

The parabola opens upward because the coefficient of \( x^2 \) is positive. So, you can expect the arms of the parabola to welcome you into its grassy embrace like a friendly hill. The vertex of the parabola \( f(x) = x^2 + 4x - 7 \) can be found by using the formula \( x = -\frac{b}{2a} \). This results in \( x = -2 \). Plugging \( x = -2 \) back into the function, you get \( f(-2) = -11 \), making the vertex \((-2, -11)\). It's like the secret treasure hidden right at the bottom of your parabola!