Question

HELP WITH MATHHHH PLEASE

Answer 1

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.