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y= -3x^2+8x+35
  = -3(x^2-8x-35)
   = -3(x-4/3)^2+121/3
 
So,vertex=(4/3,121/3)
Axis of symmetry =.   x= 4/3
Maximum point =. y = 121/3
 
x intercepts by factoring
 
y =-3x^2+8x+35
 
applying Discriminant formula
 
y= (-8+- sqrt(64+420))/-6
 
   (-8+22)/-6     &.  (-8-22)/-6
 
   -7/3.  &.  5
 
so  x  axis intercepts.  are. -7/3. &  5
 
 since axis of symmetry is x= 4/3
 
7/3+4/3  11/3
 
5-4/3=11/3
 
So, this justifies the x axis intercepts.
 
 

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