What are the vertex, focus and directrix of # y=x^2 + 3#?

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1 Answer
Roella W.
Dec 22, 2015

Vertex is (0,3), focus is (0,3.25) and directrix is y=2.75

Explanation:

The vertex is at the point where the function is at its minimum (it would be the maximum if the #x^2# factor were negative). Hence the vertex is at the point (0,3).
The focus is a distance #1/(4a)# above the vertex. It is therefore the point (0,#3*1/4#).
The directrix is the horizontal line an equal distance below the vertex and is therefore the line #y = 2*3/4#

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