What is the vertex of $(x^2)-2x-2p-(p^2)$

Question

I'm struggling to find the vertex of this quadratic: ($x^2)-2x-2p-(p^2)$ Can someone please help me?

Answer 1

As others have pointed out, you need an equation of a parabola, so there should be an equals sign somewhere. However, \begin{align*} x^2 - 2x + (\text{anything}) &= x^2 - 2x + 1 - 1 + (\text{anything}) \\ &= (x-1)^2 + (\text{anything}) -1 \text{.} \end{align*}

For your expression, $(\text{anything}) = -2p-p^2$, so if your equation is that your given expression equals zero, the vertex is $(1, -2p-p^2-1)$.

Answer 2

Let (1) the vertex be at (h, k), and (2) $f(x) = x^2 – 2x – 2p – p^2$.

By formula, $h = \dfrac {-b}{2a} = … = 1$.

$k = f(h) = f(1) = ….$