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

Answer 1

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

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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Answer 2

Jace Anderson

The vertex of the parabola ( y = x^2 + 3 ) is at ((0, 3)). The focus is at ((0, 3.25)), and the directrix is the horizontal line ( y = 2.75 ).

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.