4x Complete the square to determine the maximum or minimum value of the function defined by the expression. -x^2-10x+14 A minimum value at 25 B maximum value at 39 C maximum value at -5 D minimum value at -39

To complete the square for the quadratic expression $-x^2 - 10x + 14$, we need to rewrite it in the form $-(x - h)^2 + k$, where $h$ and $k$ are constants.<br /><br />Step 1: Factor out the negative sign from the quadratic term:<br />$-(x^2 + 10x) + 14$<br /><br />Step 2: Complete the square inside the parentheses:<br />$-(x^2 + 10x + 25) + 14 - 25$<br />$= -(x + 5)^2 - 11$<br /><br />The vertex form of the quadratic function is $y = -(x + 5)^2 - 11$. The vertex of this parabola is at $(-5, -11)$.<br /><br />Since the coefficient of the $x^2$ term is negative, the parabola opens downwards, indicating that the vertex represents the maximum value of the function.<br /><br />Therefore, the correct answer is:<br />C) maximum value at $-5$