Question

Given f(x)=2x^2+3x-8 find (b+2)

Answer 1

`\displaystyle f(b+2) = 2b^2 + 11b +6`

Explanation:

We are given the function:

`\displaystyle f(x) = 2x^2 + 3x - 8`

And we want to find:

`\displaystyle f(b + 2)`

Substitute:

`\displaystyle f(b+2) = 2(b+2)^2 + 3(b+2) - 8`

Expand and simplify:

`\displaystyle \begin{aligned}f(b+2)&= 2(b^2+4b+4)+(3b+6)-8 \\ &= (2b^2+8b+8)+(3b+6)-8 \\ &= (2b^2) + (8b+3b)+ (8+6-8) \\ &= 2b^2 + 11b + 6 \end{aligned}`

In conclusion:

`\displaystyle f(b+2) = 2b^2 + 11b +6`