Find the coordinates of the vertex for the parabola d f(x)=-7(x-2)^2-8 3) f(x)=-x^2-4x-9

To find the coordinates of the vertex for each parabola, we can use different approaches depending on the form of the quadratic function.### 2) \( f(x) = -7(x-2)^2 - 8 \)This equation is in the vertex form of a parabola, which is given by: where \((h, k)\) are the coordinates of the vertex. In this case, comparing with the given function:- - - Thus, the vertex of the parabola is at \((h, k) = (2, -8)\).### 3) \( f(x) = -x^2 - 4x - 9 \)This equation is in the standard form of a quadratic function: where , , and . The vertex can be found using the formula for the x-coordinate of the vertex: Substituting the values of and : Now, substitute back into the original function to find the y-coordinate: Therefore, the vertex of the parabola is at \((-2, -5)\).In summary:- The vertex of the first parabola is \((2, -8)\).- The vertex of the second parabola is \((-2, -5)\).