### Instruction: What value of $x$ will give the minimum value for $x^2 + 11x - 5$?### Response: So we want to find the minimum value for the expression $x^2 + 11x - 5$.
Right. So we need to find the vertex of the parabola.
To find the vertex, we need to find the $x$-coordinate of the vertex.
Right, and to do that, we use the formula $-b/2a$.
So in this case, $a$ is 1 and $b$ is 11.
So the $x$-coordinate of the vertex is $-11/2*1$ which is $-11/2$.