What is y=x^2+8x-1 in the general form?

Question

Doing Quadratics.. the problem is in standard form now but i need it in the general form

[f(x)=a(x-h)^2+k]

Please help!

Really trying to find the vertex-- if ya can get that too that would be awesome..

Thanks

Answer 1

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).