### Instruction: Two parabolas are the graphs of the equations $y=2x^2-10x-10$ and $y=x^2-4x+6$. Find all points where they intersect. List the points in order of increasing $x$-coordinate, separated by semicolons.### Response: To find the points of intersection, I need to set the two equations equal to each other and solve for $x$.
So I have $2x^2-10x-10=x^2-4x+6$, or equivalently, $x^2-6x-16=0$.
I can factor this quadratic as $(x-8)(x+2)=0$.
So the solutions for $x$ are $x=8$ and $x=-2$.
To find the corresponding $y$-coordinates, I can plug these values into either equation.
I'll use the simpler one, $y=x^2-4x+6$.
When $x=8$, $y=(8)^2-4(8)+6=38$.
When $x=-2$, $y=(-2)^2-4(-2)+6=18$.
So the points of intersection are $(-2,18)$ and $(8,38)$.