Find the points of intersection of the pairs of curves y = x² - 4 and y = 2x -1. A) (-1,-3) and (3, 5) B) (-1,-3) C) (3, 5) D) (-1,-3), (0, -1), and (3, 5) E) These curves do not intersect.

Question

Quizplus · Accepted Answer

To find the points of intersection, set the two equations equal to each other: $x^2 - 4 = 2x - 1$. Rearranging gives $x^2 - 2x - 3 = 0$, which factors to $(x + 1)(x - 3) = 0$, yielding $x = -1$ and $x = 3$. Substituting these values back into either original equation gives the points $(-1, -3)$ and $(3, 5)$.

Find the Points of Intersection of the Pairs of Curves