Find the standard form of the equation of the parabola with a vertex at the origin and a focus at (0, -4).

Question

anonymous · Answer

y =-1/4x^2

 y2 = -4x

 y2 = -16x

 y =-1/16x^2

mathmale · Answer

You might want to abandon this account and choose a more suitable user name.  Take a more positive approach!

The standard form for the equation of a vertical parabolic graph (which this one is), with info on the location of the focus, is$$4py=x^2$$ assuming that the vertex is at the origin.

You are told that the focus is at (0,-4).  Note that p is the distance from vertex to focus (or vice versa).  What is p?

Substitute that value of p into $$4py=x^2$$ and simplify the resulting equation.  Compare your result to the four possible answers.

anonymous · Answer

would p be 4?

mathmale · Answer

Yes.  Continue with this problem solution, please.

anonymous · Answer

4(4)y=x^2,

16y=x^2 ?

mathmale · Answer

that's fine.  Either leave your equation as is, or divide both sides by 16 to isolate y.

Compare your result(s) to the four given answer choices.