Question

question 9 of 10 which of the equations below could be the equation of this parabola? vertex (0, 0) a. y = -3x^2 b. x = 3y^2 c. y = 3x^2 d. x = -3y^2

Explanation:

Step1: Identify parabola orientation

The parabola opens upwards and has its vertex at the origin $(0,0)$. The general form of a parabola opening upwards or downwards is $y = ax^{2}+bx + c$, and when the vertex is at the origin $b = 0$ and $c=0$, so it is of the form $y=ax^{2}$. A parabola opening to the left - right has the form $x = ay^{2}+by + c$. Since our parabola opens upwards, we can rule out options B and D which are of the form $x = ay^{2}$.

Step2: Determine sign of coefficient

For a parabola $y = ax^{2}$, if $a>0$, the parabola opens upwards, and if $a < 0$, the parabola opens downwards. Since our parabola opens upwards, $a>0$. Option A has $a=-3$ (so it opens downwards), and option C has $a = 3$ (opens upwards).

Answer:

C. $y = 3x^{2}$