When line y=-3x+7 and parabola y= x squared - 4x+1intersect at points A and B, find the length of the line segment AB
from Kumon level I math page 191b
To find the points of intersection between the line y=-3x+7 and the parabola y=x^2-4x+1, we need to set the two equations equal to each other and solve for x:
-3x + 7 = x^2 - 4x + 1
0 = x^2 + x - 6
0 = (x + 3)(x - 2)
So the solutions are x = -3 and x = 2.
Plugging these values back into the equation of the line, we get the points of intersection A (-3, 16) and B (2, 1).
To find the length of AB, we can use the distance formula:
AB = sqrt((2 - (-3))^2 + (1 - 16)^2)
AB = sqrt(5^2 + (-15)^2)
AB = sqrt(25 + 225)
AB = sqrt(250)
AB = 5(sqrt(10))
Therefore, the length of the line segment AB is 5(sqrt(10)).