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# Analysing a parabola

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1. 20x=y^2

2. (x-3)^2 =1/2(y+1)

3. y2+14y+4x+45=0

Find the vertex, focus, and directrix of the parabola described by the above equations.

https://brainmass.com/math/calculus-and-analysis/analysing-parabola-6785

#### Solution Preview

Standard forms of the parabola are
y = x^2/4P parabola opens up
y = -x^2/4P parabola opens down
x = y^2/4p parabola opens right and
x^2= -y^2/4p shows a parabola opens left

For parabolas opening up/down, the directrix is a horizontal line in the form y = + p
For parabolas opening right/left, the directrix is a vertical line in the form x = + p
The vertex point for all of the above is (0,0)

For parabolas opening up/down, the directrix is a horizontal line in the form y = + p. ...

#### Solution Summary

The problem is solved giving all necessary mathematical steps. It will enable you to do similar problems yourself.

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