when graphed, which parabola opens downward?\n$y = - 3x^{2}$\n$y=(x - 3)^{2}$\n$y=\frac{1}{3}x^{2}$\n$y=x^{2}…
when graphed, which parabola opens downward?\n$y = - 3x^{2}$\n$y=(x - 3)^{2}$\n$y=\frac{1}{3}x^{2}$\n$y=x^{2}-3$
Answer
Explanation:
Step1: Recall parabola - opening rule
For a parabola of the form $y = ax^{2}+bx + c$ (or $y=a(x - h)^{2}+k$), if $a<0$, the parabola opens downward; if $a > 0$, it opens upward.
Step2: Analyze each option
- For $y=-3x^{2}$, $a=-3<0$, so it opens downward.
- For $y=(x - 3)^{2}=x^{2}-6x + 9$, $a = 1>0$, it opens upward.
- For $y=\frac{1}{3}x^{2}$, $a=\frac{1}{3}>0$, it opens upward.
- For $y=x^{2}-3$, $a = 1>0$, it opens upward.
Answer:
$y=-3x^{2}$