ind the coordinates of the vertex of the parabola
y = 2x2 − 4x + 9 b) One train route follows the curve
y = 2x2 − 4x + 9,
and the other follows y = x2. Assume that distance along both axes is measured in miles. The railroad wants to construct a north-south maintenance road PQ between the two routes. Where should the road be located so that it is as short as possible?
Q(x, y) =

(smaller y-value)
P(x, y) =

(larger y-value)

Question

ind the coordinates of the vertex of the parabola
y = 2x2 − 4x + 9 b) One train route follows the curve
y = 2x2 − 4x + 9,
 and the other follows y = x2. Assume that distance along both axes is measured in miles. The railroad wants to construct a north-south maintenance road PQ between the two routes. Where should the road be located so that it is as short as possible?
Q(x, y)	 =

(smaller y-value)
P(x, y)	 =

(larger y-value)

anonymous · Answer

the vertical distance between two curves is given by taking the difference between them ...$$(2x^2 - 4x + 9)  -  (x^2) = x^2 - 4x + 9 = (x-2)^2 + 5$$Looks like the two curves are 5 apart when x = 2 between (2,9) and (2,4)...

campbell_st · Answer

find the line of symmetry of the parabola....x = -b/2a

x = -(-4)/(2x2)   line of symmetry for the parabola is x = 1

substitute into th equation to find y  Vertex is (1, 7)

campbell_st · Answer

the access road will be on the line x = 1/2 mid way between the two lines of symmetry. 

find the equation of the line between the two vertices (0,0) and (1, 7) 

the equation is y = 7x.... sub x = 1/2 into the equation then Q 1/2, 3 1/2)|dw:1327804161327:dw|