Question

2.4.3 quiz: parabolas with vertices at the origin. which of the equations below could be the equation of this parabola? (0, 0) vertex a. $x = \frac{1}{12}y^{2}$ b. $y = \frac{1}{12}x^{2}$ c. $x = -\frac{1}{12}y^{2}$

Explanation:

Step1: Identify parabola orientation

The parabola opens to the right. For a parabola with vertex at the origin $(0,0)$, if it opens to the right, its standard - form equation is $x = ay^{2}$ where $a>0$, if it opens to the left, its equation is $x=-ay^{2}$ where $a > 0$, if it opens up, its equation is $y = ax^{2}$ where $a>0$, and if it opens down, its equation is $y=-ax^{2}$ where $a>0$.

Step2: Analyze the options

The given parabola opens to the right. Option A: $x=\frac{1}{12}y^{2}$ is of the form $x = ay^{2}$ with $a=\frac{1}{12}>0$, which represents a parabola opening to the right. Option B: $y=\frac{1}{12}x^{2}$ represents a parabola opening up. Option C: $x =-\frac{1}{12}y^{2}$ represents a parabola opening to the left.

Answer:

A. $x=\frac{1}{12}y^{2}$