Question

Find the constants of A and B?

Answer 1

`(a,b)=(-1,6)`

Explanation:

If `f(x)` is continuous for `-3 <=x <= 0`
then it is continuous at `x=-2` and at `x=0`

If `f(x)` is continuous at `x=-2`
then
`color(white)("XXX")f(x)=-x` at `x=-2`
`color(white)("XXX")rarr f(-2)=a * (-2)^2+b = -(-2)`
`color(white)("XXX")rarr 4a+b=2`

If `f(x)` is continuous at `x=0`
then
`color(white)("XXX")f(x)=6` at `x=0`
`color(white)("XXX")rarr f(0)=a * 0^2+b=6`
`color(white)("XXX")rarr b=6`

Combining `4a+b=2` and `b=6`
gives
`color(white)("XXX")a=-1`

Graphically here is what we have: