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

Dec 22, 2015

$\left(1 , 9\right)$ and $\left(- 3 , - 7\right)$

#### 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
${x}^{2} + 6 x + 2 = - {x}^{2} + 2 x + 8$
Moving all items to the left gives us
$2 {x}^{2} + 4 x - 6 = 0$
$\left(2 x - 2\right) \left(x + 3\right) = 0$
Therefore $x = 1$ or $x = - 3$
Substituting into one of the equations gives us
$y = - {\left(1\right)}^{2} + 2 \cdot \left(1\right) + 8 = 9$
or $y = - {\left(- 3\right)}^{2} + 2 \cdot \left(- 3\right) + 8$
$y = - 9 - 6 + 8 = - 7$
Therefore the points of intersection of the two parabolas are $\left(1 , 9\right)$ and (-3,-7)#