Question

The range of the function f(x)= x^2 + 2x - 8 is all real numbers..

Answer 1

Simplify the expression x^2+2x-8 to obtain the equation as complete square.

`\begin{gathered} x^2+2x-8=x^2+2x+1-1-8 \\ =(x^2+2x+1)-9 \\ =(x+1)^2-9 \end{gathered}`

The value of square terms is 0 or postive, so range of the expression x^2+2x-8 is,

`\lbrack-9,\infty)`

So correct option is B greater than or equal to -9.