Which among the following is the correct graphical representation of $y = - x^{2} - 1 ?$

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Solution

The correct option is D
Given: $y = - x^{2} - 1$
Since the coefficient of $x^{2}$ is negative the parabola will be downward opening.
Also, comparing with standard form of quadratic expression $y = a x^{2} + b x + c,$ we get:
$a = - 1, b = 0, c = - 1$
$& D = b^{2} - 4 a c = (0)^{2} - 4. (- 1) . (- 1) = - 4$
$\Rightarrow D < 0,$ thus no real roots for the equation.
Also, at $x = 0, y = - 1$
Thus, the graph can be drawn as:

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