Find the points of intersection (if any) of the given pair of curves. $y = x ^ { 2 }$ and y = 3x - 2.
A) (0,0)
B) There are no points of intersection.
C) (2, 4)
D) (1, 1), (2, 4)

Question

Quizplus · Accepted Answer

To find the points of intersection, set the two equations equal to each other: $x^2 = 3x - 2$. Rearrange to get a quadratic equation: $x^2 - 3x + 2 = 0$. Factoring gives $(x - 1)(x - 2) = 0$, so $x = 1$ or $x = 2$. Substituting these values back into either original equation gives the points of intersection as (1, 1) and (2, 4).

Find the Points of Intersection (If Any) of the Given y=x2y = x ^ { 2 }y=x2

Find the Points of Intersection (If Any) of the Given $y = x ^ { 2 }$