The entire graphs of the equation `y=x^2+kx-x+9` is strictly above the x-axis if and only if

Answer

`-5 lt k lt 7`

Explanation

`y=x^(2)+(k-1)x+9=(x+(k-1)/(2))^(2)+9-((k-1)/(2))^(2)`
For entire graph to be above x-axis, we should have
`9-((k-1)/(2))^(2) gt 0`
`implies k^(2)-2k-35 lt 0`
`implies (k-7)(k+5) lt 0`
`implies -5 lt k lt 7`