Write as a Vector Equality y=x^2+2 , y=x+4

Problem

y=x2+2,y=x+4

Solution

1. Set the expressions equal to find the intersection points of the two curves.

x2+2=x+4

2. Rearrange the equation into standard quadratic form by subtracting x and 4 from both sides.

x2−x−2=0

3. Factor the quadratic to solve for the xcoordinates of the intersection points.

(x−2)*(x+1)=0

4. Solve for x by setting each factor to zero.

x=2

x=−1

5. Find the corresponding ycoordinates by substituting the x values back into the linear equation y=x+4

y=2+4=6

y=−1+4=3

6. Express the solution as a vector equality where the vector of variables equals the vector of coordinates for each point.

Final Answer

([x],[y])=([2],[6]),([x],[y])=([−1],[3])

Want more problems? Check here!