Question

x^2-6x+11=y x=y+1 The system of equations above is graphed in the xy -plane. Which of the following is the y-coordinate of an intersection point (x,y) of the graphs of the two equations? A) -4 B) -2 C) 2 D) 4

Answer 1

To find the intersection point of the two graphs, we need to solve the system of equations.

Step-by-step explanation:

To find the intersection point of the two graphs, we need to solve the system of equations:

1. x^2 - 6x + 11 = y
2. x = y + 1

Substituting the value of x from the second equation into the first equation, we get:

(y+1)^2 - 6(y+1) + 11 = y

Simplifying this equation, we obtain:

y^2 - 5y + 6 = 0

Factoring the quadratic equation by splitting the middle term, we get:

(y-2)(y-3) = 0

Therefore, the values of y at the intersection points are y = 2 and y = 3.