Question

question 1 of 10

which of the equations below could be the equation of this parabola?

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

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

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

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

Explanation:

Identify the orientation of the parabola

$$ \text{The parabola opens to the right, which corresponds to the form } x = ay^2 \text{ with } a > 0. $$

Eliminate vertical parabolas

$$ y = -\frac{1}{6}x^2 \quad (\text{opens downward}) $$

$$ y = \frac{1}{6}x^2 \quad (\text{opens upward}) $$

Determine the sign of the coefficient

$$ \text{Since the parabola opens to the right (positive } x \text{-direction), } a > 0 \implies x = \frac{1}{6}y^2. $$

Answer:

• A. \(y = -\frac{1}{6}x^2\)
• B. \(x = \frac{1}{6}y^2\) (Correct answer)
• C. \(x = -\frac{1}{6}y^2\)
• D. \(y = \frac{1}{6}x^2\)