5 Given the graph below write the radical function for Ax 19

5. Given the graph below, write the radical function for Ax) 19. Find the equation in point-slope form of the line that is the perpendicular bisecto segment between (16, -4) and (-2,-76)

Solution

5)
f(x) = a*sqrt(b-x)

at x=2, f(x)=1
1 = a*sqrt(b-2)   ...eqn 1

at x=6, f(x)=0
0 = a*sqrt(b-6)
so, b = 6

put this in eqn 1
1 = a*sqrt(b-2)
1 = a*sqrt(6-2)
1 = a*2
a =1/2

so,
f(x) =   (1/2)*sqrt(6-x)

19)
slope of this line = (-76+4)/(-2-16) = -72/(-18) = 4
so,
slope of perpendicular line = -1/m = -1/4

midpoint is ((16+2)/2 , (-4+76)/2) = (10,36)

perpendicular line:
(y-36) = slope * (x-10)
(y-36) = (-1/4) * (x-10)
4y - 144 = -x+10
4y+x - 134 = 0