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

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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) About Me  (Show Source):
You can put this solution on YOUR website!
You mean for f(x)=(1/16)x^2, same as f%28x%29=%281%2F16%29x%5E2 ?

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 x=0.

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 4py=%28x-0%29%5E2%2B0. 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 4py=x%5E2.

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.
%2816%2F1%29%2Af%28x%29=%2816%2F1%29%281%2F16%29x%5E2

16%2Af%28x%29=x%5E2
and compare this to
4p%2Ay=x%5E2

f(x) clearly means the same as y.

Noting the corresponding parts, 16=4p.
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.