How do I find the equation of the parabola below? I got $y = \frac{1}{4}x^2$
But I'm quite sure about this. 
2026-03-28 03:25:20.1774668320
Simple parabola
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Your parabola must be of the type $y=ax^2$, for some $a>0$. The focus of that parabola is $F=\left(0,\frac a4\right)$. The slope of the line passing through $F$ and $(2,4a)$ is$$\frac{4a-\frac a4}2=\frac{15a}8.$$And you want it to be equal to $\frac12$. So, which $a$ should you take?