Question

Complete the square to determine the minimum or maximum value of the function defined by the expression. −x2 + 10x + 5

Answer 1

`- {x}^(2) + 10x + 5 \\ = - {x}^(2) + 10x - 25 + 5 + 25 \\ = - ( {x}^(2) - 10x + 25) + 30 \\ = \underbrace{ - {(x - 5)}^(2)}_(\leqslant 0) + 30 \\ \Rightarrow - {(x - 5)}^(2) + 30 \leqslant 30 \\ \Rightarrow Maximum \: value \: is \: 30 \: when \: x = 5`