Compete the square to determine minum or maxuim value of function define by - x2+10x+5

maximum value y = 30

Step-by-step explanation:

Given

- x² + 10x + 5

To complete the square the coefficient of the x² term must be 1

factor out - 1

= - (x² - 10x) + 5

To complete the square

add/subtract (half the coefficient of the x - term) ² to x² - 10x

= - (x² + 2 ( - 5) x + 25 - 25) + 5

= - (x - 5) ² + 25 + 5

= - (x - 5) ² + 30 ← in vertex form

y = a (x - h) ² + k

where (h, k) are the coordinates of the vertex and a is a multiplier

Hence vertex = (5, 30)

The max / min occurs at the vertex

Since a < 0 then vertex is a maximum

Hence maximum value is y = 30