Two parabolas are the graphs of the equations y=2x^2-10x-10 and y=x^2-4x-16. Find all points where they intersect. List the points in order of increasing x-coordinate, separated by semicolons.
+9 Set the two equations equal and solve.
2x^2-10x-10 = x^2-4x-16 step 1: subtract x^2 from the both sides
-x^2 -x^2
x^2-10x-10 = -4x-16 step 2: add 4x to both sides
+4x +4x
x^2-6x-10 = -16 step 3: add 16 to both sides
+16 +16
x^2-6x+6 = 0 step 4: use quadratic formula x = (-b +/- sqrt(b^2-4ac))/2a
x = (-(-6) +/- sqrt((-6)^2-4(1)(6)))/2(1) step 5: plug in
x = (6 +/- 2*sqrt(3))/2 step 6: simplify
x = 3 - sqrt(3); 3 + sqrt(3) answers
