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Write an equation of a parabola with the given vertex and focus.
vertex (-1,3); focus (-1,4)

 Jan 13, 2020
 #1
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The focal distance  is the distance between  the focus and the  vertex  = 1

 

This parabola turns upward because the  focus is a bove the  vertex

 

The form  is

 

4a ( y - k)   - (x - h)^2       where  (h,k)  is the vertex  = ( -1.3)

 

So we have that

 

4(1) ( y  - 3)  = ( x - - 1)^2

 

4 ( y - 3) = (x + 1)^2           divide both sides by 4

 

y  - 3  =(1/4) (x + 1)^2     add 3 to both sides

 

y = (1/4) (x + 1)^2  +  3

 

cool cool cool

 Jan 13, 2020

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