The graph of $y = 4 x^{2} + 3 x + 7$

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.
$y = 4 x^{2} + 3 x + 7$
consider $4 x^{2} + 3 x + 7 = 0$
$Δ = b^{2} - 4 a c = 9 - 4 (4) 7 = - 1920$
$∴$ the equation has no roots .
$∴ y = 0 \Rightarrow$ it doesn't cut the x-axis anywhere and lies above it.

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