What is the equation of the parabola that has a vertex at # (-4, 6) # and passes through point # (-8,70) #?

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Answer 1 · 2016-02-02T11:48:42

#y =4x^2 +8x +22#

The general form of a parabola is #y = ax^2 + bx +c# which can also be rewritten as #y = n(x-h)^2 +k# where #(h,k)# is the vertex.

Thus the parabola is #y = n(x+4)^2 +6# and we can use the other given point to find #n#

#70 = n(-8+4)^2 +6#

#70 =16n +6#

#n = 64/16 =4#

#:.y = 4(x+4)^2 +6#

#y =4x^2 +8x +22#