Find where the line y = 2x intersects the curve y = x^2.

Question

I tried to set the 2 equations equal to each other to solve for x then for y

y = x^2     and    y = 2x  

leads to    xrt2 - 2x = 0    so x = 0 and 2

therefore when x = 0, y = 0  and when x = 2   y = 4.

Could someone please advise me if points of intersection are (0,0) and (2,2); as my next step is to calculate the area enclosed by the line and the curve. I'd really like to know if I am on the right track before I go any further.

Answer 1

Your working is correct up to the line,

therefore when x = 0, y = 0  and when x = 2   y = 4.

Your two points of ontersection are (0,0) (x = 0, y = 0) and (2, 4) (x = 2, y = 4)