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

Options

A. `k lt 7`
B. `-5 lt k lt 7`
C. `k gt -5`
D. None of these

Explanation

To determine the values of \( k \) for which the graph of the equation \( y = x^2 + kx - x + 9 \) is strictly above the \( x \)-axis, we can follow these steps:

### Step 1: Rewrite the equation
The given equation can be rewritten as:
\[ y = x^2 + (k - 1)x + 9 \]
This is a quadratic equation in the standard form \( ax^2 + bx + c \) where:
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