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The entire graph of the equation y=x^2+k...

The entire graph of the equation `y=x^2+k x-x+9` in strictly above the `x-a xi s` if and only if `k<7` (b) `-5-5` (d) none of these

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The correct Answer is:
`-5 lt k lt 7`
`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`
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