+96 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?
+23252 Finding the vertex of y = x2 - 2x + 3 y = x2 + 4x + 10
y - 3 = x2 - 2x y - 10 = x2 + 4x
y - 3 + 1 = x2 - 2x + 1 y - 10 + 4 = x2 + 4x + 4
y - 2 = (x - 2)2 y - 6 = (x + 2)2
Vertex: (2, 2) Vertex: (-2, 6)
To find the distaces between the vertices: distance = sqrt( (x2 - x1)2 + (y2 - y1)2 )
= sqrt( (-2 - 2)2 + (6 - 2)2 )
= sqrt( (-4)2 + (4)2 )
= sqrt( 16 + 16 )
= sqrt( 32 )
