The graph above could be a representation of which of the following equations?

y = x + 11

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y = x^{2} - 2 x - 9

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y = (x - 1)^{2} - 9

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y = x^{2}

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Solution

The correct option is D $y = (x - 1)^{2} - 9$
The roots of the quadratic equation are $x = - 2$ and $x = 4$ .
Hence, the equation is $y = (x + 2) (x - 4)$
$= x^{2} - 2 x - 8$
$= (x - 1)^{2} - 9$

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