Something funny is that the x value of the vertex lies directl in the middle of the x intercepts
so
we see the x intercepts or 0's at x=8 and 2
the average is x=5
so find f(5) to find the y value of the vertex
f(5)=(5-8)(5-2)
f(5)=(-3)(3)
f(5)=-9
vertex is at (5,-9)
the actual way the teacher wants is to expand then compltete the square to get into the form f(x)=a(x-h)^2+k where the vertex is (h,k)
but whatever
verrtex is at (5,-9)
Let a and b represent the heights of the corresponding buildings (in meters).
... a = b +271 . . . . . . . a is 271 meters taller than b
... 2b -a = 211 . . . . . . if a is subtracted from twice b, the result is 211
Use the expression for a in the first equation to substitute for a in the second.
... 2b - (b+271) = 211
... b = 482 . . . . . . . . . . . simplify and add 271
... a = b +271 = 753
Building a is 753 meters tall; building b is 482 meters tall.
