# How do you determine the values of the coefficients a and b that will give a minimum value of the area, #S#, of the region enclosed by the curve #y=-x^2+ax+b# (which passes through point (1,2)) and the curve #y=(1/2)x^2#?

##### 1 Answer

#### Explanation:

Calling

the intersection points between

Solving for

with

so the intersection points are at

The enclosed area is

Substituting now

So finally

Attached a plot showing