If \(y = x^{2} - 6x + 11\) is written in the form \(y = a(x - h)^{2} + k\), find the value of \((a + h + k)\).

If \(y = x^{2} - 6x + 11\) is written in the form \(y = a(x - h)^{2} + k\), find the value of \((a + h + k)\).

Answer Details

We can start by completing the square to rewrite the quadratic equation in the form given. \begin{align*} y &= x^{2} - 6x + 11\\ &= (x^{2} - 6x + 9) + 2\\ &= (x - 3)^{2} + 2 \end{align*} Now we can see that the equation is in the desired form, with \(a = 1\), \(h = 3\), and \(k = 2\). Therefore, \begin{align*} (a + h + k) &= (1 + 3 + 2)\\ &= 6 \end{align*} So the value of \((a + h + k)\) is 6.