The graph of $y = x^{2} + 3 x + 4$

lies entirely below the x-axis.

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lies entirely above the x-axis.

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cuts the x-axis.

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touches the x-axis and lies below it.

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Solution

The correct option is B lies entirely above the x-axis.
Compare $a x^{2} + b x + c = 0$ with the given equation, then $a = 1, b = 3, c = 4$
We get $b^{2} - 4 a c < 0$ for the given equation which implies it has imaginary roots
and since $a > 0$ , the graph lies entirely above x axis.

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