Question

question 6 of 10

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

a. (y = 3x^2)
b. (x = -3y^2)
c. (y = -3x^2)
d. (x = 3y^2)

Explanation:

Identify the orientation of the parabola

$$ \text{The parabola opens to the left, which means its axis of symmetry is horizontal (the } x\text{-axis).} $$

Determine the standard equation form

$$ \text{A parabola with vertex at } (0,0) \text{ opening horizontally has the form } x = ay^2. $$

Determine the sign of the coefficient

$$ \text{Since the parabola opens to the left (towards negative } x\text{), the coefficient } a \text{ must be negative: } a < 0. $$

$$ \text{Thus, the equation must be of the form } x = -3y^2. $$

Answer:

• A. \(y = 3x^2\)
• B. \(x = -3y^2\) (Correct answer)
• C. \(y = -3x^2\)
• D. \(x = 3y^2\)