Question

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

Answer 1

`(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)#