Question

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

Explanation:

Step1: Identify parabola orientation

The parabola opens to the left. Parabolas of the form $y = ax^{2}$ open upwards (if $a>0$) or downwards (if $a < 0$), and parabolas of the form $x=ay^{2}$ open to the right (if $a>0$) or to the left (if $a < 0$). Since our parabola opens to the left, it must be of the form $x = ay^{2}$ with $a<0$.

Step2: Select the correct equation

Among the options, the equation of the form $x = ay^{2}$ with $a<0$ is $x=- 3y^{2}$.

Answer:

D. $x = -3y^{2}$