Question

question 5 of 10
which of the equations below could be the equation of this parabola?

a. ( y = -\frac{1}{6}x^{2} )
b. ( y = \frac{1}{6}x^{2} )
c. ( x = \frac{1}{6}y^{2} )
d. ( x = -\frac{1}{6}y^{2} )

Explanation:

Step1: Determine the standard form of the parabola

The parabola opens to the right. The standard form of a parabola that opens to the right with vertex \((h,k)\) is \(x=a(y - k)^{2}+h\). Here, the vertex is \((0,0)\), so the equation is \(x = ay^{2}\).

Step2: Analyze the sign and coefficient

Since the parabola opens to the right, \(a>0\). Among the options, only \(x=\frac{1}{6}y^{2}\) (Option C) has \(a=\frac{1}{6}>0\) and is in the form \(x = ay^{2}\) with vertex \((0,0)\). Options A and B are in the form \(y = ax^{2}\) (which are parabolas opening up or down), and Option D has \(a=-\frac{1}{6}<0\) (would open to the left).

Answer:

C. \(x = \frac{1}{6}y^{2}\)