Answer: The correct statement is (B). Both parabolas open downward, and \(y=-3x^2\) is wider than \(y=-7x^2.\)
Step-by-step explanation: The equations of the two parabolas are as follows:
\(y=-3x^2~~~~~~~~~~~~~(i)\\y=-7x^2~~~~~~~~~~~~~(ii)\)
The standard equation of a parabola is given by
\(y=a(x-h)^2+k.\)
If a < 0, then the parabola open downwards and if a > 0, then the parabola open upwards.
From equation (i), we have
\(y=-3x^2\\\\\Rightarrow y=-3(x-0)^2+0,\)
so a = -3 < 0, so the parabola (i) open downwards.
From equation (ii), we have
\(y=-7x^2\\\\\Rightarrow y=-7(x-0)^2+0,\)
so a = -7 < 0, so the parabola (ii) open upwards.
Also, since -3 > -7, so the parabola (i) is wider than the parabola (ii).
Therefore, both parabolas open downward, and \(y=-3x^2\) is wider than \(y=-7x^2.\)
The graphs of the parabolas are shown in the attached figure.
Thus, (B) is the correct ption.
