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Question

Let A be the vertex of the graph of the equation y=x^2 - 2x + 3 . Let B be the vertex of the graph of the equation y=x^2 + 4x + 10 . What is the distance between A and B?

Accepted Answer

Completing the square in each equation results in the equations y=(x - 1)^2 + 2 and y=(x + 2)^2 + 6. Thus, A = (1, 2) and B = (-2, 6). We can then find the distance between A and B to be (1-(-2))^2 + (2-6)^2 = 9+16 =5.