Question

which of the equations below could be the equation of this parabola?
a. y = -\frac{1}{2}x^{2}
b. x = \frac{1}{2}y^{2}
c. y = \frac{1}{2}x^{2}

Explanation:

Step1: Identify parabola orientation

The parabola opens upwards and has its vertex at the origin $(0,0)$. The general form of a parabola opening upwards with vertex at the origin is $y = ax^{2}$, where $a>0$.

Step2: Analyze options

Option A: $y=-\frac{1}{2}x^{2}$ has $a =-\frac{1}{2}<0$, so it opens down - wards. Option B: $x=\frac{1}{2}y^{2}$ is a parabola that opens to the right. Option C: $y = \frac{1}{2}x^{2}$ has $a=\frac{1}{2}>0$ and is of the form $y = ax^{2}$, so it opens upwards.

Answer:

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