Answer:
(6,38)
Step-by-step 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: [tex]min = C - \frac{B^{2} }{4A}[/tex]
So, in our equation,
A = 1/2
B = 2
C = 8
If we enter those values in the formula, we get:
[tex]min = 8 - \frac{2^{2} }{4 * \frac{1}{2} } = 8 - \frac{4}{2} = 8 - 2 = 6[/tex]
Now that gives us the value of x = 6.
We enter that in the given equation to obtain the y coordinate of the minimum:
[tex]y = \frac{x^{2} }{2} + 2x + 8 = \frac{6^{2} }{2} + 2(6) + 8 = 18+12+8 = 38[/tex]
So y = 38 when x = 6.
Minimum point is then (6,38)
