The vertex is at the point (0,0) and the focus at the point (0, 1/8). This is given to us. Both the vertex and focus are separated by a vertical distance in the positive direction.
This means that the parabola opens upward. The vertex form of the equation for a parabola that opens upward is:
y = a(x - h)^2 + k, where the point
(h, k) is the vertex of the parabola.
Plug the vertex given into the above equation.
y = a(x - 0)^2 + 0
y = ax^2 + 0
y = ax^2
What is a?
Note: a = 1/(4f), where f is the distance from the vertex to the focus or simply as given in the focus point above 1/8.
Let f = 1/8
a = 1/4(1/8)
a = 1/(1/2)
a = 2
The equation we want is
y = 2x^2.
f(x) = 2x^2
Choice A is the answer.
