Find the equation of a parabola with vertex (-4,2) and directrix y=5?

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Mar 7, 2018

Answer:

#y = -1/12(x-(-4))^2+2#

Explanation:

The vertex form for the equation of a parabola with a horizontal directrix is:

#y = 1/(4f)(x-h)^2+k" [1]"#

where #(h,k)# is the vertex and the equation of the directrix is, #y = k-f" [2]"#

Substitute the vertex #(-4,2)# into equation [1]:

#y = 1/(4f)(x-(-4))^2+2" [1.1]"#

Substitute #k = 2# and #y = 5# into equation [2]:

#5=2-f#

#f = -3#

Substitute #f = -3# into equation [1.1]:

#y = -1/12(x-(-4))^2+2" [1.2]"#

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