Question

I
If f(x) = 2x² - x -9 , find:
a. f(-2)
b. f(x-2)
c. r?

Answer 1

`f(x) = 2 {x}^(2) - x - 9 \\ \\ a) \: plug \: x = - 2 \\ f( - 2) = 2 * {( - 2)}^(2) - ( - 2) - 9 \\ f( - 2) = 2 * 4 + 2 - 9 \\ f( - 2) =8 + 2 - 9 \\ f( - 2) =10 - 9 \\ \huge \red{ \boxed{ f( - 2) =1}} \\ \\ b) \: \: plug \: x = x - 2 \\ f(x - 2) = 2 {(x - 2)}^(2) - (x - 2) - 9 \\ f(x - 2) = 2 {( {x}^(2) - 4x + 4 )} - x + 2- 9 \\ f(x - 2) = 2 {x}^(2) - 8x + 8 - x + 2- 9 \\ \purple{ \boxed{\bold{f(x - 2) = 2 {x}^(2) - 9x + 1}}} \\ \\ c) \: \: plug \: x = r \\ \orange{\boxed{\bold{f(r) = 2 {r}^(2) - r - 9}}}`