The parabolas defined by the equations \(y = -x^2 - x + 1 \) and \(y = 2x^2 - 1 \)intersect at points (a, b) and (c, d), where c is greater than or equal to a. What is c - a? Express your answer as a common fraction.
+618 In order to find the points where the parabola intersects, we set the equations to equal to each other in order to find a common x term. We get:
-x^2-x+1=2x^2-1
Simplfying, we get 3x^2+x-2=0, and using the quadratic formula, we get that x can be equal to 2/3 or -1.
These are the x-values of the coordinates of the intersection points, or a and c. SInce c is greater than a, we get that c=2/3, and a=-1. 2/3-(-1) is equal to 1 2/3, or 5/3, which is our answer.
Ans=5/3
+618 In order to find the points where the parabola intersects, we set the equations to equal to each other in order to find a common x term. We get:
-x^2-x+1=2x^2-1
Simplfying, we get 3x^2+x-2=0, and using the quadratic formula, we get that x can be equal to 2/3 or -1.
These are the x-values of the coordinates of the intersection points, or a and c. SInce c is greater than a, we get that c=2/3, and a=-1. 2/3-(-1) is equal to 1 2/3, or 5/3, which is our answer.
Ans=5/3
