What is the vertex of the graph of the function \( f(x)=x^{2}+8 x-2 \) ? \( (-4,18) \) \( (0,-2) \) \( (-8,-2) \) \( (-4,-18) \)

To find the vertex of the quadratic function \( f(x) = x^{2} + 8x - 2 \), you can use the vertex formula \( x = -\frac{b}{2a} \). Here, \( a = 1 \) and \( b = 8 \), so we have \( x = -\frac{8}{2 \cdot 1} = -4 \). Substituting \( x = -4 \) back into the function gives \( f(-4) = (-4)^{2} + 8(-4) - 2 = 16 - 32 - 2 = -18 \). Therefore, the vertex is \( (-4, -18) \). Did you know that the vertex of a quadratic function represents the minimum or maximum point on its graph? In this case, since the parabola opens upwards (the coefficient of \( x^2 \) is positive), the vertex at \( (-4, -18) \) is indeed the lowest point on the graph! If you’re looking to sketch the graph yourself or solve similar equations in the future, remember this tip: Completing the square is another effective method for finding the vertex. Simply rearranging \( f(x) \) into vertex form can also help you identify the vertex without directly using those formulas. Happy graphing!