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Modulus Function

The graph of ...

Question

The graph of $y = x^{2} + 7 x + 12$

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 C cuts the x-axis.
$y = x^{2} + 7 x + 12$
$= x^{2} + 4 x + 3 x + 12$
$= x (x + 4) + 3 (x + 4)$
$= (x + 3) (x + 4)$
$∴ y = 0 \Rightarrow x = - 3, - 4$
$∴$ it cuts x-axis at (-3,0) and (-4,0)

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