Write as a Vector Equality y=x^2 , y=2x+3

Problem

y=x2,y=2*x+3

Solution

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

x2=2*x+3

2. Rearrange into standard quadratic form by moving all terms to one side of the equation.

x2−2*x−3=0

3. Factor the quadratic expression to solve for the xcoordinates.

(x−3)*(x+1)=0

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

x=3

x=−1

5. Find the corresponding y-coordinates by substituting the x values back into either original equation.

For *x=3,y=(3)2=9

For *x=−1,y=(−1)2=1

6. Express as a vector equality by writing the coordinates as vectors.

([x],[y])=([3],[9])

([x],[y])=([−1],[1])

Final Answer

([x],[y])=([3],[9]),([−1],[1])

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