We can't square each side because that creates a radical function, which we don't want. Instead, let's divide each side by 16:
y^2/16=(16x)/16y216=16x16
x=y^2/16x=y216
Let's rewrite this as x=1/16 y^2x=116y2 since it will be easier to help us find what we need.
We don't have much to go off of, but we can find pp. You might know this as the distance from the vertex of a parabola to both its focus and its directrix. We can find pp by setting the scale factor equal to 1/(4p)14p:
1/16=1/(4p)116=14p
4p=164p=16
p=4p=4
Before we go any further, we should know that the graph faces the right. How do we know this? 1) The slope is positive, and 2) xx, not yy, is isolated on one side of the equation.
The vertex is (0,0)(0,0) because there are no translations in the function. When a parabola has a vertex at the origin, the focus is (0,p)(0,p). The focus is always within the parabola, so a right-facing parabola has a focus to the right of the vertex. Our focus, therefore, would be 4 units to the right of the vertex and is (0,4)(0,4). Finally, the directrix is x=-4x=−4 because directrix is pp units away from the parabola, but in the opposite direction.
