SOLUTION: Identify the focus, directrix, and axis of symmetry of f(x)=1/16x^2. If possible please add steps. Thanks!

Question 1049994: Identify the focus, directrix, and axis of symmetry of f(x)=1/16x^2. If possible please add steps. Thanks!
Answer by josgarithmetic(39617) (Show Source): You can put this solution on YOUR website!
You mean for f(x)=(1/16)x^2, same as ?

The focus and the directrix are the (only slightly) tough parts to solve for. If you understand parabolas well enough you immediately recognize symmetry axis here is .

The basic form of the equation of a parabola with vertical symmetry axis and parabola with vertex as a minimum AND on the origin is like . That is what you would derive using the definition of parabola... Yes, your function f(x) has its vertex at the origin, (0,0).

That equation is more tightly written as .

What does "p" mean in that equation?
p is the distance of the vertex to either the focus or to the directrix.
Adjust your function to correspond to the form just shown.

and compare this to

f(x) clearly means the same as y.

Noting the corresponding parts, .
What is the meaning of p, again?

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Review the Definition of a Parabola and the use and meaning of the terms, Directrix, and Focus; and be sure you understand the Distance Formula.

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One small correction: The absolute value of p is the distance between the vertex and either to the focus or directrix.
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