Two parabolas are the graphs of the equations y = 2x^2 - 7x - 1 and y = 8x^2 - 2x - 5. Give all points where they intersect. List the points in order of increasing x-coordinate, separated by semicolons.
+128408 Set the equations equal
2x^2 - 7x - 1 = 8x^2 - 2x - 5 rearrange as
6x^2 + 5x - 4 = 0 factor as
(3x + 4) ( 2x - 1) = 0
Set each factor to 0 and solve for x and the x intersection points are
-4/3 and 1/2
When x = -4/3 y = 2(-4/3)^2 - 7(-4/3) - 1 = 107 / 9
When x = 1/2 y = 2 (1/2)^2 - 7(1/2) - 1 = -4
The points are
(-4/3, 107/9) and ( 1/2 , -4)
