Final answer:
The vertex of the parabola is (0,0), the focus is (0,4), the directrix is y = -4, and the focal width is 1/4 units.
Step-by-step explanation:
The given equation is 1/16x² = y. This is the equation of a parabola. In order to find the vertex, focus, directrix, and focal width of the parabola, we need to rewrite the equation in standard form: y = ax² + bx + c. Comparing this with the given equation, we can see that a = 1/16, b = 0, and c = 0.
The vertex of the parabola is given by the formula x = -b/2a = -0/(2*(1/16)) = 0. So the coordinates of the vertex are (0,0).
Since the value of b is 0, the parabola opens either upwards or downwards. In this case, since a is positive (1/16 is greater than 0), the parabola opens upwards. The focus of the parabola is located at a distance of 1/4a = 1/(4*(1/16)) = 4 units above the vertex. So the coordinates of the focus are (0,4).
The directrix of the parabola is located at a distance of 1/4a = 1/(4*(1/16)) = 4 units below the vertex. So the equation of the directrix is y = -4.
The focal width of the parabola is given by the formula 4a = 4*(1/16) = 1/4 units.