Write as a Vector Equality y=2x^2+4x+3 , y=x-2

Problem

y=2*x2+4*x+3,y=x−2

Solution

1. Identify the components of the vector equation by setting the two expressions for y equal to each other to find the intersection points.

2*x2+4*x+3=x−2

2. Rearrange the equation into standard quadratic form by subtracting x and adding 2 to both sides.

2*x2+3*x+5=0

3. Represent the system of equations as a single vector equation where the vector of functions is equal to a zero vector or a target vector.

([y],[y])=([2*x2+4*x+3],[x−2])

4. Formulate the equality by expressing the relationship between the variables x and y in a single vector statement.

([x],[y])=([x],[2*x2+4*x+3])

Final Answer

([y],[y])=([2*x2+4*x+3],[x−2])

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