What are x and y if #y=x^2+6x+2# and # y=-x^2+2x+8#?

1 Answer
Roella W.
Dec 22, 2015

#(1,9)# and #(-3,-7)#

Explanation:

I interpret the question as asking what values of x and y will satisfy both expressions. In that case, we can say that for the required points
#x^2 +6x +2 = -x^2 +2x +8#
Moving all items to the left gives us
#2x^2 +4x -6 = 0#
#(2x -2)(x + 3) = 0#
Therefore #x=1# or #x=-3#
Substituting into one of the equations gives us
#y = -(1)^2 +2*(1) +8 = 9#
or #y = -(-3)^2 + 2*(-3) +8#
#y = -9 -6 +8 = - 7#
Therefore the points of intersection of the two parabolas are #(1,9)# and (-3,-7)#

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