Question

Which of the following is the minimum value of the function? y=1/2x2+2x+8

Answer 1

(6,38)

Explanation:

Since the x² term is positive, we know there will be a minimum point.

The formula to find the minimum in an equation of the type y = Ax² + Bx + C

is the following:
`min = C - (B^(2) )/(4A)`

So, in our equation,

A = 1/2

B = 2

C = 8

If we enter those values in the formula, we get:

`min = 8 - (2^(2) )/(4 * (1)/(2) ) = 8 - (4)/(2) = 8 - 2 = 6`

Now that gives us the value of x = 6.

We enter that in the given equation to obtain the y coordinate of the minimum:

`y = (x^(2) )/(2) + 2x + 8 = (6^(2) )/(2) + 2(6) + 8 = 18+12+8 = 38`

So y = 38 when x = 6.

Minimum point is then (6,38)