y=x²+8x-1, y=x²+8x+16-16-1, y=(x+4)²-17
y=f(x)=(x+4)²-17 so h=-4 and k=-17.
The vertex is the highest or lowest point on the curve, depending on whether the parabola is shaped like an upside-down U or an upright U. In this case, it’s upright, so the vertex is the lowest point. This means y or f(x) has its lowest or minimum value. In this case y can’t go below -17, and this happens when x=-4 (the value of h) and when y=-17 (the value of k). So when the function is in general or standard form, (h,k) is the vertex, and in this case it’s (-4,-17).